4.6 Physical Sciences
PHY421: Laser physics and advanced optics


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Course Outline

Introduction
to
Lasers:
Principles
of
laser
action,
threshold
criteria,
building
blocks
of
a
laser,
Basic
properties
of
laser
light,
coherence,
directionality,
photon
flux,
Lasers
and
Masers,
Survey
of
laser
applications.

AtomField
interaction:
Einstein’s
A
and
B
coefficients,
Coherent
and
incoherent
emissions,
threelevel
and
four
level
schemes,
Rate
equation
model
for
laser,
Optical
pumping.

Gaussian
beam
and
Optical
resonators:
Propagation
of
Gaussian
beam,
ABCD
Matrix,
linear
and
ring
resonators,
Confocal
cavity,
stability
analysis
of
cavity,
cavity
modes,
quality
factor.

Types
of
Lasers:
Gas
lasers:
CO_{2}
and
Arion,
Liquid
dye
laser,
Solid
state
lasers
(Ruby
laser,
Nd:YAG),
semiconductor
lasers,
edge
emitting
and
vertical
cavity
surface
emitting
lasers,
Pulsed
laser
operation,
Qswitching,
saturable
absorption,
mode
locking,
Ultrafast
lasers.

Nonlinear
Optics:
Polarization
properties
of
lasers,
Jones
Matrix
formalism,
Nonlinear
effects,
second
harmonic
generation,
Kerr
effect,
Pockel
effect,
self
focusing
and
defocusing,
Optical
isolators.

Topics
in
Advanced
Optics:
Semiclassical
theory
of
laser,
Correlation
function
and
coherence
concepts,
Photon
statistics
in
cavities,
one
atom
laser,
Laser
cooling
and
trapping
of
atoms,
Introduction
to
optical
lattices
and
atom
optics.
Recommended Reading

A.
E.
Siegman,
Lasers,
University
Science
Books
(1986).

K.
K.
Sharma,
Optics,
Principles
and
applications,
Academic
Press
USA
(2006).

J.
T.
Verdeyen,
Laser
Electronics,
03rd
edition,
Prentice
Hall,
(1995).

K.
Thyagarajan
and
A.K.
Ghatak,
Lasers:
Theory
and
Applications,
Springer
(1981).

M.
Sargent
III,
M.O.
Scully
and
W.E.
Lamb,
Jr.,
Laser
Physics,
Westview
Press
(1978).

L.
Mandel
and
E.
Wolf,
Optical
Coherence
and
Quantum
Optics,
Cambridge
University
Press
(1995).

B. B. Laud,
Lasers
and
Nonlinear
Optics,
John
Wiley
&
Sons
Inc.
(1985).

C.
CohenTannoudji,
J.
DupontRoc,
and
G.
Grynberg,
AtomPhotonInteractions:
Basic
Processes
and
Applications,
WileyInterscience
NY
(1998).
PHY422: Computational methods in physics


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Course Outline

Solution
of
Linear
Systems
AX = B:
Matrix
arithmetic,
Gaussian
Elimination,
LU
Factorization,
Error
estimation
and
Residual
Correction
method,
Jacobi
method.
Numerical
Diagonalization
of
matrices.
Singular
value
decomposition.
Eigenvalue
problem.

Interpolation:
Polynomial
interpolation,
Hermite
interpolation,
spline
interpolation.

Differentiation:
Differentiation
of
interpolating
polynomials,
method
of
undetermined
coefficients.

Numerical
Integration:
Composite
Trapezoidal
and
Simpson’s
Rule,
Gaussian
quadrature,
Monte
Carlo
Integration.

Solution
of
Nonlinear
Equations
f(x) = 0:
Iteration,
Bracketing
methods
for
locating
a
root,
NewtonRaphson
and
Secant
methods.

Solution
of
Ordinary
Differential
Equations,
Euler’s
method,
RungeKutta
methods,
Initial
and
Boundary
Value
Problems.

Optimization:
Minimization,
minimization
in
several
dimensions,
Monte
Carlo
Markov
Chains
based
methods.

Partial
differential
equations:
Diffusion
equation,
Wave
equation,
Poisson
equation.
Finite
element
and
relaxation
methods.
Recommended Reading

H.
M.
Antia,
Numerical
Methods
For
Scientists
And
Engineers,
02nd
edition,
Birkhauser
Basel
(2002).

Numerical
Recipes
in
C:
The
Art
of
Scientific
Computing,
W.
H.
Press,
S.
A.
Teukolsky,
W.
T.
Vellerling
and
B.
P.
Flannery,
Cambridge
University
Press
(1992).
PHY423: Mathematical methods for physicists


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Course Outline

Complex
algebra:
Functions
of
complex
variables,
CauchyRiemann
conditions,
Cauchys
integral
theorem,
Laurent
expansion,
singularities,
mapping,
conformal
mapping.
Calculus
of
residues,
Dispersion
relations,
method
of
steepest
descent.

Gamma
and
Beta
functions:
Gamma
function,
definition
and
properties,
Stirlings
series,
Beta
function,
Incomplete
Gamma
function.

Differential
equations:
Partial
differential
equations,
First
order
differential
equations,
separation
of
variables,
singular
points,
series
solutions
with
Frobenius
method,
a
second
solution,
nonhomogenneous
equations,
Greens
function,
Heat
flow
and
diffusion
equations.

SturmLiouville
theory:
Self
adjoint
ordinary
differential
equations,
Hermitian
operators,
GramSchmidt
orthogonalization,
completeness
of
eigenfunctions,
Greens
function
eigenfunction
expansion.

Special
functions:
Bessel
functions
of
the
first
kind,
orthogonality,
Neumann
functions,
Hankels
functions,
Asymptotic
expansions,
Spherical
Bessel
functions.
Legendre
functions,
generating
function,
recurrence
relations,
orthogonality,
alternate
definitions,
associated
Legendre
functions,
spherical
harmonics,
Hermite
functions,
Laguerre
functions.

Fourier
series:
General
properties,
applications
of
Fourier
series,
properties
of
Fourier
series,
Gibbs
phenomenon,
discrete
Fourier
transform,
relation
with
fast
Fourier
transforms.

Integral
transforms:
Fourier
integral,
Fourier
transforms,
inversion
theorem,
Fourier
transform
of
derivatives,
convolution
theorem,
Laplace
transform
and
its
relation
to
Fourier
transform.
Laplace
transform
solution
to
differential
equations.
convolution
theorem,
Inverse
Laplace
transform.

Introduction
to
integral
equations:
Integral
transforms,
generating
functions,
Neumann
series,
separable
Kernels,
HilbertSchmidt
theory.
Recommended Reading

H.
J.
Weber
and
G.
B.
Arfken,
Essential
Mathematical
Methods
for
Physicists,
Academic
Press
(2004).

D.
A.
McQuarrie,
Mathematical
Methods
for
Scientists
and
Engineers,
Viva
Books
(2009).

Mary
L.
Boas,
Mathematical
Methods
in
the
Physical
Sciences,
Wiley
(2005).
PHY424: Relativistic quantum mechanics and quantum field theory


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Course Outline

Relativistic
Quantum
Mechanics
:
KleinGordon
equation,
Dirac
equation
and
its
plane
wave
solutions,
significance
of
negative
energy
solutions,
spin
angular
momentum
of
the
Dirac
particle.
Nonrelativistic
limit
of
Dirac
equation,
Electron
in
electromagnetic
fields,
spin
magnetic
moment,
spinorbit
interaction,
Dirac
equation
for
a
particle
in
a
central
field,
fine
structure
of
hydrogen
atom.
Propagator
Theory
for
Schrodinger,
Klein
Gordon
and
Dirac
Theory.

Relativistic
Quantum
Field
Theory
:
Canonical
Quantization
of
real
and
complex
scalar
fields.
Quantization
of
Spin
half
field.
Dirac
,
Weyl
and
Majorana
fields.
Quantization
of
Spin
1
field.
Covariant
perturbation
theory,
Wick’s
Theorem.
Scattering
matrix.
Tree
level
Feynman
diagrams,
calculation
of
Correlation
functions,
decay
widths
and
scattering
cross
sections,
Basics
of
QED.
Recommended Reading

Sakurai,
Advanced
Quantum
Mechanics(Pearson).

A.
Lahri
and
P.
Pal,
A
First
Book
of
Quantum
Field
Theory(Narosa).

M.
Peskin
and
Schroeder,
Introduction
to
Quantum
Field
Theory(Levant
books,
Kolkata).

H.
Mandl
and
G.
Shaw
Quantum
Field
Theory,(Wiley,
New
York).

Mark
Srednicki,
Quantum
Field
Theory,
Cambridge
University
Press,
(2007).

V.P
Nair,
Quantum
Field
Theory:
A
Modern
Perspective,
Springer.
PHY601: Review of classical mechanics


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Course Outline

Lagrangian
and
Hamiltonian
formulation
of
classical
mechanics,
two
body
central
force
problem,
rigid
body
motion,
special
theory
of
relativity,
phase
space
formulation
of
classical
mechanics.
Nonlinearity
and
chaos.
(The
methodology
of
the
course
will
be
based
on
learning
by
problem
solving)
Recommended Reading

H.
Goldstein,
Classical
mechanics,
03rd
edition,
AddisonWesley,
Cambridge
MA
(2001).

L.
D.
Landau
and
E.M.
Lifshitz,
Mechanics,
03rd
edition,
Butterworth
Heinemann
(1976).
PHY602: Review of electrodynamics


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Course Outline

Gauss
law,
Electrostatics,
boundary
value
problems,
Greens
function,
magnetostatics,
Electrodynamics,
Faraday’s
law,
Amperes
law,
Maxwell’s
equations,
covariant
form
of
Maxwell
equations,
electromagnetic
waves
and
their
propagation,
retarded
potentials,
radiation.
(The
course
will
be
based
on
learning
by
problem
solving)
Recommended Reading

J.
D.
Jackson,
Classical
Electrodynamics,
3rd
edition,
New
York:
Wiley.

D.
J.
Griffiths,
Introduction
to
Electrodynamics,
03rd
edition,
PrenticeHall
NJ
(1999).

L.
D.
Landau
and
E.M.
Lifshitz,
The
Classical
theory
of
fields,
4th
edition,
Pergamon
(1994).
PHY603: Review of statistical mechanics


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Course Outline

Review
of
thermodynamics.
Equation
of
state,
equilibrium
and
stability,
Van
der
Waal
gas,
phase
transitions,
Laws
of
thermodynamics.
Carnot
engine,
heat
pump.
Disorder
and
Entropy.
Phase
space.
Probability
density
and
functions
of
a
random
variable,
Liouville
Theorem.

Microcanonical
ensemble,
Boltzmann
probability.
Canonical
ensemble,
partition
function,
Monoatomic
ideal
gas,
virial
theorem,
energy
fluctuations,
collection
of
harmonic
oscillators,
statistics
of
paramagnetism,
polyatomic
gas.
Grand
canonical
ensemble,
density
and
energy
fluctuations.
Density
matrix
formalism.
Examples.

Quantum
statistics.
Indistinguishable
particles,
symmetric
vs
antisymmetric
wave
function.
Ideal
Bose
gas
and
ideal
Fermi
gas
in
quantum
ensembles
and
thermodynamic
properties,
Blackbody
radiation.
BoseEinstein
condensation.
Specific
heat
of
solids.
Pauli
paramagnetism.
Introduction
to
Phase
transitions.
Recommended Reading

R
K
Pathria,
Statistical
Mechanics,
02nd
edition,
ButterworthHeinemann
(1996).

K
Huang,
Statistical
Mechanics,
02nd
edition,
Wiley
(1987).

L.D
Landau
and
E.M.Lifshitz,
Course
in
Theoretical
Physics
Vol.
5,
03rd
edition,
ButterworthHeinemann
(1984).
PHY604: Review of quantum mechanics


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Course Outline

Classical
vs.
Quantum
Mechanics,
Simple
2state
QM
system.
Hilbert
Spaces,
Operators.
Observables

Compatible
Observables,
Tensor
Product
Spaces,
Uncertainty
Relations.
Position,
Momentum
and
Translation.
Eigenvalue
Problems.

Time
Evolution
(Quantum
Dynamics).
Schroedinger,
Heisenberg
and
Interaction
Pictures;
Energytime
Uncertainty,
Interpretation
of
Wavefunction.
Ehrenfest,
Quantization,
Path
Integrals.
Quantum
Particles
in
Potential
and
EM
Fields

Gauge
Invariance,
AharanovBohm.

Angular
Momentum:
SO(3)
vs. SU(2).
Lie
Algebra
and
Representations
of
SU(2).
Spherical
Harmonics.
Addition
of
Angular
Momenta.
Tensor
Operators
and
WignerEckardt
Perturbation
Theory:
RayleighSchroedinger
(Nondegenerate
Timeindependent)
Perturbation
Theory.
Examples
in
Hydrogen
Atom.

Symmetry
groups
in
QM.
Parity.
Time
reversal.
Identical
particles

permutations.
Pauli
exclusion.
Central
field
approximation.
Hartree
equations.
Scattering:
Born
approximation.
Spherical
waves.
partial
wave
scattering.
Lowenergy
scattering,
bound
states,
resonances.
Coulomb
scattering.

Relativistic
quantum
mechanics:
Dirac
equation.
KleinGordon
equation.
Relativistic
particles
and
group
theory.
Solutions
to
Dirac:
free
particle,
relativistic
Hydrogen
atom.
Recommended Reading

L.Schiff,
Quantum
mechanics,
03rd
edition,
McGrawHill
(1968).

J.J.Sakurai,
Modern
quantum
mechanics,
AddisonWesley
(1993).

C.CohenTannoudji,
Quantum
mechanics
Vols
1
and
2,
WileyInterscience
(2006).
PHY622: Topics in mathematical methods


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Course Outline

Linear
Algebra:
Vector
spacs,
inner
products,
linear
maps,
vector
algebra,
factor
algebras,
total
matrix
algebras,
decomposition
of
algebras,
polynomial
algebra,
operator
algebra,
Hermitian
and
unitary
operators,
projection
operators,
representation
of
algebras,
matrices,
determinants.

Group
Theory:
Homomorphism
and
isomorphism
of
groups,
generators
of
continuous
groups,
matrix
representations:
reducible
and
irreducible,
rotation
groups
SO(2)
and
SO(3),
special
unitary
group
SU(2),
homogeneous
Lorentz
group.
Introduction
to
group
representations.
Unitary
representations
of
SO(3).

Differential
equations:
linear
and
nonlinear
differential
equations,
nonlinear
differential
equations
relevant
in
physics.
KleinGordon;
SineGordon
equation;
KdV
equations;
soliton
solutions.
Stochastic
differential
equations,
Langevin
equation,
Fokker
Planck
equations
Recommended Reading

H.
J.
Weber
and
G.
B.
Arfken,
Essential
Mathematical
Methods
for
Physicists,
Academic
Press
(2004).

D.
A.
McQuarrie,
Mathematical
Methods
for
Scientists
and
Engineers,
Viva
Books
(2009).

Sadri
Hassani,
Mathematical
Physics,
Springer
(2013)

J.
V.
Jose,
and
E.
J.
Saletan,
Classical
Dynamics:
A
Contemporary
Approach,
Cambridge
University
Press
(2002).

C.
Gardiner,
Handbook
of
Stochastic
Methods
for
Physics,
Chemistry
and
the
Natural
Sciences,
Springer
(2004).
PHY631: Quantum computation and quantum information


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Course Outline

Introducing
quantum
mechanics.
Quantum
kinematics,
quantum
dynamics,
quantum
measurements.
(The
course
is
self
contained
and
does
not
assume
a
background
in
quantum
mechanics).
Single
qubit,
multiqubits,
gates.
Density
operators,
pure
and
mixed
states,
quantum
operations,
environmental
effect,
decoherence.
Quantum
nocloning,
quantum
teleportation.

Cryptography,
classical
cryptography,
introduction
to
quantum
cryptography.
BB84,
B92
protocols.
Introduction
to
security
proofs
for
these
protocols.

Introduction
to
quantum
algorithms.
DeutschJozsa
algorithm,
Grover’s
quantum
search
algorithm,
Simon’s
algorithm.
Shor’s
quantum
factorization
algorithm.

Errors
and
correction
for
errors.
Simple
examples
of
error
correcting
codes
in
classical
computation.
Linear
codes.
Quantum
error
correction
and
simple
examples.
Shor
code.
CSS
codes.

Quantum
correlations,
Bell’s
inequalities,
EPR
paradox.
Theory
of
quantum
entanglement.
Entanglement
of
pure
bipartite
states.
Entanglement
of
mixed
states.
Peres
partial
transpose
criterion.
NPT
and
PPT
states,
bound
entanglement,
entanglement
witnesses.

Physical
realization
of
qubit
system.
Different
implementations
of
quantum
computers.
NMR
and
ensemble
quantum
computing,
Ion
trap
implementations.
Optical
implementations.
Recommended Reading

M. A. Nielsen
and
I .L. Chuang,
Quantum
Computation
and
Quantum
Information,
Cambridge
University
Press
(2000).

J. Preskill’s
Lecture
Notes
on
Quantum
Information
http://www.theory.caltech.edu/people/preskill/ph229/
PHY632: Advanced experiments in physics


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Course Outline
This course is intended for Advanced MS (Physics Major) students with an interest in
gaining experience in an experimental physics research group. The course can
be offered every semester, with a set of instructors drawn from the available
experimental research groups. The mode of instruction will comprise a combination of
lectures, tutorials and minor research projects to be carried out in the research
lab of the concerned instructor currently the available modules are as follows
out of which depending upon the instructs at least two will be included in the
course.

NMR
Spectroscopy
Lab:
Applying
the
Fourier
transform
to
the
NMR
signal.
Digital
data
processing,
Nyquist
theorem,
Discrete
Fourier
transform,
FFT
algorithm,
window
functions
and
apodization.
Physical
basis
of
the
NMR
signal,
phase
correction,
phase
cycling.
RedfieldBloch
relaxation
theory
and
Master
equation
approach
to
identifying
relaxation
processes
in
systems
of
two
and
three
coupled
spins.
The
basic
2D
FTNMR
experiment
and
application
to
finding
the
structure
of
a
biomolecule.
Pulsed
field
gradients
and
understanding
diffusion
processes
in
polymer
chains.
Selective
pulse
rotations,
composite
pulses
and
implementation
of
an
NMR
Quantum
Computing
algorithm.

Femtosecond
Laser
Lab:
Experiments
with
cw
laser,
cavity
stability,
beam
parameters,
divergence,
diameter,
intracavity
frequency
doubling.
Experiments
with
femtosecond
laser:
measurement
of
femtosecond
laser
parameters,
pulse
duration,
autocorrelation,
spectral
width,
repetition
rate,
beam
diameter,
divergence,
application
of
fs
pulses
to
measure
speed
of
light
in
vacuum,
air
and
in
glass.
Pumpprobe
spectroscopy,
interferometric
stability,
ultrafast
phenomenon
measured
by
fs
pump
probe
setup.

Low
Temperature
Physics
Lab:
This
lab
will
focus
on
low
noise
electronics.
Projects
will
involve
integrating
different
electronic
equipments
in
one
Labview
programme.
As
an
example
varying
gate
voltage
from
a
DAQ
card
output
and
measuring
the
conductance
using
a
lockin
amplifier
(
a
mock
device
like
a
commercial
JFET
or
MOSFET
will
be
used).
Students
will
also
do
some
hands
on
Radiofrequency
electronics
like
designing
coplanar
waveguides
on
a
PCB
.
They
will
be
expected
to
understand
concepts
like
noise
figures
and
noise
temperatures,
develop
cryogenic
amplifiers
to
be
tested
at
liquid
nitrogen
temperatures.

Solid
State
Physics
Lab:
Students
will
make
new
compounds
by
mixing
up
starting
materials/chemicals.
These
could
be
superconducting,
magnetic,
or
could
show
other
interesting
properties.
Students
will
also
do
characterization
and
imaging
of
these
and
other
materials
using
a
Scanning
Electron
Microscope
(SEM).
Specifically
students
will
look
at
gold
nanoparticles
and
the
wonder
material
graphene
using
the
SEM.
Recommended Reading

M. Sayer
and
A. Mansingh,
Measurement,
Instrumentation
and
Experiment
Design
in
Physics
and
Engineering,
PrenticeHall
of
India
Pvt.Ltd
(2004).

D. M. Pozar,
Microwave
Engineering,
03rd
edition,
Wiley
(2004)

E. Fukushima
and
S .B. Roeder,
Experimental
Pulse
NMR:
A
nuts
and
bolts
approach,
Westview
Press
(1993)

R. C. Richardson
&
E. N. Smith,
Experimental
Techniques
In
Condensed
Matter,
Westview
Press
(1998).
PHY633: Mesoscopic physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
quantum
mechanical
notation.
Basic
problems
in
QM
like
transmission
via
a
potential
well,
density
of
states
Fermi
golden
rule,
Landau
quantization
of
electrons
in
magnetic
field
and
AharonovBohm
effects.

Review
of
semiconductor
concepts
.
Overview
of
fabrication
techniques
of
mesoscopic
devices

2D
electrons
confined
to
semiconductor
heterostructures.
Quantized
Hall
phenomena
and
associated
ShubnikovdeHass
Oscillations.
Phenomenological
theory
along
Laughlin’s
gauge
invariance
arguments
,
WidomSreda
thermodynamic
formulations,
followed
by
Thouless’s
winding
number
approach.
Scaling
theory
of
localization
in
1D
and
2D.
2D
systems
showing
metallic
phases
due
to
ee
interactions.
Wigner
crystals
in
extremely
dilute
2D
electron
systems
in
high
magnetic
fields.
Other
2D
electron
systems
like
graphene,
electrons
on
helium
surfaces
and
organic
transistors.

Landauer
transmission
formalism.
Application
of
formalism
to
explain
quantized
conductance
of
devices
like
quantum
point
contacts.
Weak
localization
nd
AharonovBohm
effect
in
gold
rings
and
other
systems.
Violation
of
Kirchhoff’s
circuit
laws
for
quantum
conductors.

Overview
of
superconductors.
London
equations
.
Classic
flux
quantization
experiments
of
Doll
&
Nabauer
,
Deaver
&
Fairbank.
Josephson
effect
and
SQUIDS.
Landau
Zener
tunneling
and
Macroscopic
quantum
effects
in
SQUID
based
devices.

Nanomechanical
systems.
Applications
to
mass
sensing
filters
etc.
Dissipation
phenomena
in
nanomechanical
resonators
and
possibility
of
achieving
macroscopic
quantum
states
in
mechanical
systems.

Spintronics.
JohnsonSilsbee
experiments
,
Datta
Das
Transistors
,
Giant
magnetoresistance
and
applications
.
Recommended Reading

Y.
Murayama,
Mesoscopic
Systems,
Wiley
VCH
(2001).

S. Datta,
Electronic
Transport
in
Mesoscopic
Systems,
Cambridge
University
Press
(1997).

A.
Cleland,
Foundations
of
Nanomechanics,
Springer
(2001).

M. Ziese
and
M. J. Thornton,
Spin
Electronics
(Lecture
Notes
in
Physics),
Springer
(2001).
PHY634: NMR in physics and biology


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline
The course is intended for advanced MS and PhD students with an interest in
applications of nuclear magnetic resonance (NMR) to problems in structural biology,
medicine and physics. The course will also include tutorials and handson experience with
actual data obtained from the NMR facility.

Physical
basis
of
the
NMR
signal.
Bloch
equations
and
the
macroscopic
view.
Zeeman
splitting,
Larmor
precession,
Resonance
phenomenon,
Spin
echo.
The
NMR
spectrometer.
Basic
hardware
components
including
the
magnet,
rf
transmitter,
probe
and
receiver.
Fourier
transform
NMR.
Digitizing
the
signal
using
the
DFT.
The
FFT
algorithm.
The
rf
pulse
and
its
excitation
profile.
Data
processing
techniques
for
resolution
enhancement
and
S/N
improvement

The
chemical
shift.
The
diamagnetic
effect
and
the
paramagnetic
term.
Chemical
shift
anisotropy.
Hydrogen
bonding.
Scalar
coupling.
Investigation
of
exchange
processes.
The
Nuclear
Overhauser
effect
(NOE).
The
density
matrix
and
the
product
operator
formalism.
Rf
pulses
and
evolution.
Coherence
transfer.
Origins
of
relaxation
in
systems
of
coupled
spins.
Application
to
gaining
information
about
dynamics
in
biomolecules
over
biologically
relevant
timescales.
The
TROSY
experiment.

The
basic
2DNMR
experiment.
Extension
to
three
dimensions.
Assignment
strategies,
triple
resonance
experiments
and
structure
determination
protocols
for
proteins.

Overview
of
new
and
exciting
developments
in
NMR:
Nucleic
acids
and
macromolecular
assemblies.
Drug
design
and
discovery.
Fast
acquisition.
Metabolic
studies
by
NMR.
Residual
dipolar
couplings.
Protein
folding
by
NMR.

Pulsed
field
gradients
and
studies
of
diffusion
by
NMR.
Applications
to
the
physics
of
polymers,
nonNewtonian
fluids
and
macromolecular
crowding.

Basics
of
Magnetic
Resonance
Imaging
(MRI).
Use
of
magnetic
field
gradients
to
create
a
correspondence
between
intensity,
frequency
or
phase,
and
spatial
coordinates.
fMRI
(Functional
MRI)
and
imaging
processes
in
the
brain
Basics
of
flow
and
MR
angiography.
Recommended Reading

M.
H.
Levitt,
Spin
DynamicsBasics
of
Nuclear
Magnetic
Resonance,
02nd
edition,
Wiley
(2008).

J.
Cavanagh,
W.
J.
Fairbrother,
A.
G.
Palmer
III
and
N.
J.
Skelton,
Protein
NMR
spectroscopy,
principles
and
practice,
2nd
edition,
Academic
Press
(2006).

B. Blumich,
Essential
NMR:
For
scientists
and
engineers,
Springer
(2005).

J. Keeler,
Understanding
NMR
spectroscopy,
2nd
edition,
Wiley
(2010).

K. V. R
Chary
and
G. Govil,
NMR
in
Biological
Systems:
From
molecules
to
human,
Springer
(2008).

M. L. Lipton
and
E. Kanal,
Totally
accessible
MRI,
Springer
(2008).

D. W. McRobbie,
E. A. Moore,
M. J. Graves
and
M. R. Prince,
MRI
from
Picture
to
Proton,
2nd
edition,
Cambridge
University
Press
(2007).
PHY635: Gravitation and cosmology


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
special
relativity
and
Newtonian
gravity.

Equivalence
principle,
local
inertial
frames.

The
metric
tensor.
Measurements
of
lengths
and
synchronization
of
clocks.

Coordinate
transformations,
manifolds
and
tensors.

Christöffel
symbols,
geodesic
equation,
geodesic
deviation
equation
and
the
curvature
tensor.

Stressenergy
tensor,
Bianchi
identities,
Einstein’s
equation.

Maxwell’s
equations
in
curved
space
time,
stressenergy
tensor
for
the
electromagnetic
field.

Synchronous
coordinates.

Gravitational
field
of
a
point
mass,
Schwarzschild
metric
and
black
holes.
Orbits
around
a
point
mass,
precession
of
perihelion,
lensing
equation.
The
horizon
and
the
singularity
in
the
Schwarzschild
metric.

Gravitational
field
of
a
star,
interior
and
exterior
solutions,
gravitational
field
of
a
rotating
body,
Kerr
metric.

Post
Newtonian
(PN)
and
Post
Minkowski
(PM)
description
of
theories
of
gravity.
Experimental
tests
of
the
general
theory
of
relativity.

Linearized
field
equations,
gauge
freedom.
scalar,
tensor
and
vector
modes.
Gravitational
waves.

Symmetries
and
Killing
vectors.

The
cosmological
principle,
RobertsonWalker
metric,
Friedmann
equations.
Solutions
of
the
Friedmann
equations.

Cosmological
redshift,
distances
in
cosmology.
Observational
constraints
from
distance
measurement.

CosmicMicrowave
Background
Radiation
(CMBR)
in
the
standard
cosmological
model,
flatness
and
horizon
problems,
inflationary
scenarios.

Brief
overview
of
the
thermal
history
of
the
universe
and
formation
of
large
scale
structure.
Recommended Reading

L.
D.
Landau
and
E.
M.
Lifshitz,
Classical
Theory
of
Fields,
ButterworthHeinemann
(1980).

C.
W.
Misner,
K.
S.
Thorne
and
J.
A.
Wheeler,
Gravitation,
W.
H.
Freeman
(1973).

S.
Weinberg,
Gravitation
and
Cosmology,
John
Wiley
&
Sons
(1972).

T.
Padmanabhan,
Gravitation:
Foundations
and
Frontiers,
Cambridge
University
Press
(2010).

S.
Weinberg,
Cosmology,
Oxford
University
Press
(2008).

J.
B.
Hartle,
Gravity:
An
introduction
to
Einstein’s
General
Relativity,
Benjamin
Cummings
(2003).

B.
F.
Schutz,
A
first
course
in
general
relativity,
Cambridge
University
Press
(2009).

P.
J.
E.
Peebles,
Principles
of
Physical
Cosmology,
Princeton
University
Press
(1993).

T.
Padmanabhan,
Theoretical
Astrophysics:
Volume
3,
Galaxies
and
Cosmology,
Cambridge
University
Press
(2002).

S. Dodelson,
Modern
Cosmology,
Academic
Press
(2003).
PHY636: Advanced condensed matter physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introduction
and
Motivation:
Energy,
length
and
time
scales
in
solid
state;
complexity
and
emergent
behavior;
brief
review
of
key
concepts
in
quantum
mechanics
and
statistical
mechanics.

Second
quantization:
Quantum
fields
as
creation
and
annihilation
operators;
Fermi
and
Bose
statistics;
commutation
and
anticommutation
relations.

Tightbinding
models
and
their
applications:
oneband
and
multiband
models;
electronic
structure
and
crystal
lattices;
metals
and
insulators;
magnetic
materials.

Transition
metal
compounds:
spin,
charge
and
orbital
degrees
of
freedom
and
their
interplay;
manganites;
cuperates;
pnictides.

Phase
Transitions:
Examples
of
phase
transitions;
GinzburgLandau
approach;
Renormalization
group
methods.

Special
Topics
(some
of
them
will
be
as
term
papers):
Strong
coupling
expansion;
MonteCarlo
methods;
Exactdiagonalization
methods;
BCS
theory
of
superconductivity;
doubleexchange
and
Kondolattice
models;
BoseEinstein
condensation;
Graphene
and
the
quantum
Hall
effect.
Recommended Reading

M. Tinkham,
Introduction
to
Superconductivity,
Dover
Publications
(2004).

C. J. Pethick
and
H. Smith,
BoseEinstein
Condensation
in
Dilute
Gases,
Cambridge
University
Press
(2008).

G.
D.
Mahan,
Many
Particle
Physics,
Springer
(2010).

N.
Goldenfeld,
Lectures
on
Phase
Transitions
and
the
Renormalization
Group,
Westview
Press
(1992).

A.
L.
Fetter
and
J.
D.
Walecka,
Quantum
Theory
of
Many
Particle
Systems,
Dover
Publications
(2003).

P.
Fazekas,
Lecture
Notes
on
Electron
Correlation
and
Magnetism,
World
Scientific
(1999).

N.
W.
Ashcroft
and
N.
D.
Mermin,
Solid
State
Physics,
Brooks
Cole
(1976).
PHY637: Astrophysics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Brief
survey
of
astronomical
objects.

An
overview
of
different
types
of
telescopes
and
detectors
and
units
of
measurement.

Coordinates
and
time
keeping.

Gravitation
dynamics
and
the
solar
system,
dynamics
of
systems
with
a
large
number
of
masses,
collisionless
limit.
Dynamical
friction
and
violent
relaxation.

Fluid
mechanics,
hydrostatics,
waves
in
fluids,
shocks,
turbulence.

Magnetohydrodynamics:
basic
equations,
magnetic
Reynolds
number,
flux
freezing.
Generation
and
amplification
of
magnetic
fields.

Radiative
processes,
scattering
of
radiation,
radiation
transfer.
Faraday
rotation,
dispersion
and
scintillation.

Physics
of
stars,
stellar
structure,
the
HertzsprungRussel
diagram,
stellar
evolution,
synthesis
of
elements.

Stellar
remnants:
white
dwarf
stars,
Chandrasekhar
mass
limit,
neutron
stars
and
pulsars,
mass
limit
for
neutron
stars
and
the
equation
of
state.
Black
holes,
stellar
black
holes
and
supermassive
black
holes.

Inter
Stellar
Medium:
cold,
warm
and
hot
phases,
emission
nebulae
and
photoionization
equilibrium,
molecular
clouds
and
star
formation.
magnetic
fields
in
galaxies.

Galaxies:
structure
and
dynamics
of
galaxies,
star
formation
and
the
inter
stellar
medium,
evolution
of
galaxies.
Rotation
curves
and
dark
matter.

Inter
galactic
medium:
observations,
models
of
evolution.

Clusters
of
galaxies:
galaxies,
missing
mass,
intra
cluster
medium,
SunyaevZel’dovich
effect,
Xray
emission
from
hot
gas,
gravitational
lensing.

Cosmological
principle
and
models
of
the
universe.
Hubble’s
law.
Cosmological
redshift,
distances
in
cosmology.
Observational
constraints
from
distance
measurement.

CosmicMicrowave
Background
Radiation
(CMBR)
in
the
standard
cosmological
model,
flatness
and
horizon
problems,
inflationary
scenarios.

Thermal
history
of
the
universe:
primordial
nucleosynthesis,
decoupling
of
neutrinos,
electronpositron
annihilation.
Star
formation
and
feedback,
reionization
of
the
inter
galactic
medium.

Evolution
of
density
perturbations
and
formation
of
large
scale
structure.
Recommended Reading

M. Harwit,
Astrophysical
Concepts,
Springer
(2006).

J. Binney
and
M. Merrifield,
Galactic
Astronomy,
Princeton
University
Press
(1998).

T. Padmanabhan,
Theoretical
Astrophysics:
Volumes
13,
Cambridge
University
Press
(2002).

A.
R.
Choudhuri,
Astrophysics
for
Physicists,
Cambridge
Universe
Press
(2010).

F. H. Shu,
Physical
Universe:
An
introduction
to
astronomy,
University
Science
Books
(1982).

P. Schneider,
Extragalactic
astronomy
and
cosmology:
An
introduction,
Springer
(2006).

G. B. Rybicki
and
A.
P.
Lightman,
Radiative
Processes
in
Astrophysics,
WileyVCH
(1985).

L. Spitzer
Jr.,
Physical
processes
in
the
interstellar
medium,
WileyVCH
(1998).

J.Binney
and
S. Tremaine,
Galactic
Dynamics,
Princeton
University
Press
(2008).

P.
J.
E.
Peebles,
Principles
of
Physical
Cosmology,
Princeton
University
Press
(1993).

S.
Weinberg,
Cosmology,
Oxford
University
Press
(2008).
PHY638: Physics of fluids


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Ideal
fluids:
Conservation
of
mass
and
the
equation
of
continuity,
Euler’s
equation,
hydrostatics,
energy
and
momentum
flux,
potential
flow,
incompressible
fluids.
Waves
in
an
incompressible
fluid.

Viscous
fluids:
Equation
of
motion,
energy
dissipation
in
an
incompressible
fluid.
Reynolds
numbers.
Laminar
wake.

Turbulence:
Stability
of
flows,
instability
of
tangential
discontinuities,
transition
to
turbulence.
Description
of
turbulent
flows
using
correlation
functions.
Turbulent
flow
and
the
phenomenon
of
separation
with
examples.

Thermal
conduction
in
fluids,
heat
transfer
in
a
boundary
layer,
heating
of
a
body
in
a
moving
fluid,
convection.

Diffusion:
The
equations
of
fluid
dynamics
for
a
mixture
of
fluids,
diffusion
of
suspended
particles
in
a
fluid.

Surface
phenomena
like
capillary
waves.

Sound:
Sound
waves,
the
energy
and
momentum
of
sound
waves,
reflection
and
refraction,
propagation
of
sound
in
a
moving
medium,
absorption
of
sound.

Shocks:
Propagation
of
disturbances
in
a
moving
gas,
surfaces
of
discontinuity,
junction
conditions,
thickness
of
shock
waves.

One
dimensional
gas
flow:
flow
of
gas
in
a
pipe,
flow
of
gas
through
a
nozzle,
onedimensional
travelling
waves,
characteristics
and
Riemann
invariants.

Physics
of
strong
explosions,
SedovTaylor
solution.
Recommended Reading

L.
D.
Landau
and
E.
M.
Lifshitz,
Fluid
Mechanics:
Volume
6
(Course
of
Theoretical
Physics),
ButterworthHeinemann
(1987).

G.
K.
Batchelor,
An
Introduction
to
Fluid
Dynamics,
Cambridge
University
Press
(2000).
PHY639: Topics in biophysics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
essential
physical
principles
and
laws,
forces,
energy,
laws
of
thermodynamics;
Life
and
its
physical
basis.

The
cell
and
its
components:
membranes,
cytoskeleton,
organelles.
The
central
role
of
macromolecules:
proteins,
nucleic
acid,
carbohydrates.
Brownian
motion
and
viscosity
and
their
influence
on
particle
motion
in
the
cell.

Cell
movement,
movements
of
proteins,
cytoskeleton,
molecular
motors,
actin,
myosin,
active
and
passive
transport,
adhesion,
cell
signalling,
Brownian
motion,
viscosity,
physics
at
low
Reynolds
number.

The
Cell
Membrane:
lipid
bilayers,
Liposomes.

Structure
and
function
of
proteins,
structural
organization
within
proteins:
primary,
secondary,
tertiary,
and
quartenary
levels
of
organization,
stability
of
proteins,
protein
folding
problem,
free
energy
and
denaturation,
motions
within
proteins,
how
enzymes
work,
measurement
of
binding
and
thermodynamic
analysis.

Nucleic
acids
and
genetic
information,
DNA
double
helix,
How
structure
stores
information,
DNA
replication
process,
From
DNA
to
RNA
to
protein,
DNA
packing,
DNA
denaturation,
unzipping,
RNA
transcription.

Neurons,
action
potential,
HodgkinHuxley
analysis,
ion
channels
and
pumps,
biophysics
of
the
synapse,
Neural
networks.

Fluorescent
imaging
techniques,
electron
microscopy,
xray
crystallography,
NMR
spectroscopy,
atomic
force
microscopy,
optical
tweezers.
Recommended Reading

R. Phillips,
J. Kondev
and
J. Theriot,
Physical
biology
of
the
cell,
Taylor
&
Francis
(2008).

M. Daune,
Molecular
biophysics
structures
in
motion,
Oxford
University
Press
(1999).
PHY640: Nonequilibrium statistical mechanics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Qualitative
comparison
of
equilibrium
and
nonequilibrium
systems.
Review
of
thermodynamic
ensembles,
phase
space
density,
Liouville
equation.

Langevin
equation,
fluctuationdissipation
theorem,
velocity
autocorrelation.

Master
equations,
ChapmanKolmogorov
equation,
KramersMoyal
expansion,
Discrete
Markov
processes,
solution
of
Master
equation,
stationary
distribution,
detailed
balance,
EinsteinSmoluchowski
equation.

FokkerPlanck
equation,
OrnsteinUhlenbeck
(OU)
distribution,
the
diffusion
equation.
Diffusion
in
three
dimensions,
Diffusion
in
a
finite
region,
reflecting
and
absorbing
boundaries.
Brownian
motion,
Wiener
processes,
relationship
between
OU
and
Wiener
processes,
Survival
probability,
mean
firstpassage
time.

Diffusion
in
a
potential,
Langevin
equation
in
an
external
potential,
Kramer’s
equation,
Brownian
oscillator,
Smoluchowski
equation,
Kramer’s
escape
rate.
Diffusion
in
a
magnetic
field.

GreenKubo
formulas,
Dynamic
mobility,
power
spectral
density,
WienerKhinchin
theorem,
white
and
colored
noise.
Recommended Reading

V.
Balakrishnan,
Elements
of
Nonequilibrium
Statistical
Mechanics,
Ane
Books,
New
Delhi
(2008).

R.
Zwanzig,
Nonequilibrium
Statistical
Mechanics,
Oxford
University
Press
(2004).

N.
G.
van
Kampen,
Stochastic
Processes
in
Physics
and
Chemistry,
North
Holland
Amsterdam
(1985).

H.
Risken,
The
FokkerPlanck
Equation:
Methods
of
Solution
and
Applications,
SpringerVerlag
Berlin
(1996).
PHY641: Advanced classical mechanics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Aim:
An
advanced
course
in
classical
mechanics
that
lays
down
the
foundation
for
further
study
of
modern
physics,
from
quantum
mechanics
to
statistical
mechanics
to
nonlinear
dynamics.
Stress
will
be
on
the
more
modern
formalisms,
concepts,
and
techniques
of
classical
mechanics
that
find
applications
in
a
variety
of
fields.

Topics:

Lagrangian
Formulation
of
Mechanics;
Constraints
and
Configuration
Manifolds;
Symmetries
and
Conservation
laws

Hamiltonian
Formulation
of
Mechanics;
Hamilton’s
Equations
of
Motion
(Symplectic
Approach)

Canonical
Transformations;
ActionAngle
Variables;
Poisson
brackets
and
Invariants;
Integrable
Systems

Canonical
Perturbation
Theory

Adiabatic
Invariants;
Rapidly
Varying
Perturbations

KAM
theorem;
Nonintegrability
and
Chaos
in
Hamiltonian
Systems

Introduction
to
Continuum
Dynamics
and
Classical
Fields
(SineGordon
Equation;
KleinGordon
equation;
Solitons)

Semiclassical
Quantization
(EinsteinBrillouinKeller
Quantization;
Gutwiller
Trace
Formula)
Recommended Reading

J. V. Jose
and
E. J. Saletan,
Classical
Dynamics

A
Contemporary
Approach,
Cambridge
University
Press
(1998).

M. Tabor,
Chaos
And
Integrability
In
Nonlinear
Dynamics:
An
Introduction,
WileyInterscience
(1989).
PHY642: Nonequilibrium thermodynamics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
equilibrium
thermodynamics:
Laws
of
thermodynamics,
Gibbs
equation,
Legendre
transforms
of
thermodynamic
potentials.
Stability
of
equilibrium
states.

Classical
Irreversible
thermodynamics
(CIT):
Generalized
forces
and
fluxes,
Local
equilibrium
hypothesis,
Onsagar
reciprocity
relations,
stationary
states,
minimum
entropy
production,
applications,
limitations
of
CIT.

Coupled
transport
phenomena:
Thermoelectric
effect,
Seebeck
effect,
diffusion
through
a
membrane.

Finitetime
thermodynamics:
Finite
time
Carnot
cycle,
Generalized
potentials,
thermodynamic
length,
criteria
for
optimal
performance.
Quantum
models
of
heat
engines.

Extended
irreversible
thermodynamics:
Heat
conduction,
Fourier
vs.
Cattaneo’s
law,
extended
entropy,
nonlocal
terms,
applications.
Recommended Reading

G. Lebon,
D. Jou
and
J. CasasVazquez,
Understanding
Nonequilibrium
Thermodynamics,
Springer
(2008).

H.B.
Callen,
Thermodynamics
and
an
Introduction
to
Thermostatistics,
2nd
edition,
John
Wiley
and
Sons
(1985).

I.
Prigogine,
Introduction
to
Thermodynamics
of
Irreversible
Processes,
3rd
edition,
Interscience
Publishers
(1967).

S.R.
De
Groot
and
P.
Mazur,
Nonequilibrium
Thermodynamics,
Dover
Publications,
New
York
(2011).
PHY643: Electrodynamics of continuous media


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
Maxwell’s
equations
in
free
space.
Definition
of
auxiliary
fields
in
Matter
and
Maxwell’s
equations
in
materials.

Electrostatics
of
conductors,
Brief
overview
of
thermodynamic
relations
and
Electrostatics
of
Dielectrics.

Steady
currents
in
matter,
Drude
model,
Galvanomagnetic
phenomena,
Thermoelectric
and
Thermomagnetic
Phenomena
Static
magnetic
fields,
gyromagnetic
phenomena

Superconductivity
(London’s
Phenomenological
formulation)
Quasi
static
effects
,
skin
effect
overview
of
circuit
theory

Electromagnetic
waves
in
material
media.
Kramers
Kronig
relations
for
AC
susceptibilities
Wave
guides.
Recommended Reading

L.D.
Landau
&
E.M.
Lifshitz
Electrodynamics
of
Continuous
media,
2nd
edition
Elsevier
(1981).

R.
Becker,
Electromagnetic
fields
&
Interactions,
Dover
Publications
(1982).

M. W. Zemansky,
Heat
&
Thermodynamics,
7th
edition,
McGraw
Hill
(1997).

N.
W.
Ashcroft
&
N.
D.
Mermin,
Solid
State
Physics,
Holden
Day
(1976).
PHY644: Foundations of quantum mechanics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introduction
Quantum
theory
(QT)
is
empirically
a
very
successful
theory;
there
is
however
an
apparent
lack
of
understanding
of
the
theory.
This
is
mostly
due
to
the
fact
that,
unlike
the
spacetime
structure,
the
cut
between
the
ontology
and
epistemology
in
QT
is
difficult
to
resolve.
The
two
fundamental
concepts–the
nonlocal
correlations
(entanglement)
between
spacelike
separated
systems
and
the
indistinguishability
(nonorthogonality)
of
quantum
states–is
widely
believed
to
separate
QT
from
classical
theories.
In
this
course
we
take
a
foundational
approach
to
QT
from
the
outside:
i.e.,
since
classical
theories
are
completely
devoid
of
entanglement,
it
is
compared
with
various
foil
theories
that
are
also
nonlocal
and
indistinguishable
in
the
sense
of
QT,
such
that
their
special
nature
in
the
theory
can
be
quantified.
The
two
concepts
will
be
explained
in
this
course
through
the
variety
of
topics
it
has
motivated
in
the
field
of
quantum
information
and
computation,
or
vice
versa.

Mathematical
Review:
The
review
of
the
Hilbertspace
formulation
of
quantum
mechanics,
quantum
states,
quantum
dynamics,
and
measurements
qubits,
blocksphere
representation,
Pauli
algebra,
pure
versus
mixed
states,
tensorproduct,
entanglement,
purification,
VECing
an
operator,
quantum
operations,
LOCC,
unitary
versus
nonunitary
dynamics,
decoherence,
positive
versus
completely
positive
maps,
Kraus
decomposition

Correlations:
EPR
paradox,
the
realism
and
nosignaling
principle,
the
hidden
variable
theories,
the
violation
of
Belltype
inequalities
by
entangled
states
(CHSH,
Mermin,
and
Svetlichny
inequalities),
Nonlocal
PR
box,
simulating
quantum
correlations,
shared
randomness,
entanglement
and
computational
complexity

Indistinguishability:
discrimination
and
estimation
of
unknown
quantum
states,
von
Neumann
versus
POVM
measurements,
quantum
tomography,
nature
of
probabilities
in
QT,
contextuality,
Gleason’s
theorem,
KochenSpecker
theorem,
compression
of
information,
Von
Neumann
entropy,
accessible
information
and
Holevo’s
theorem,
bit
commitment,
efficient
simulation
of
Hamiltonian
dynamics
Recommended Reading

A. Peres,
Quantum
Theory:
Concepts
and
Methods,
Kluwer
Dordrecht
(1995).

J. S. Bell,
Speakable
and
Unspeakable
in
Quantum
Mechanics,
Cambridge
University
Press
(2004).

M. A.
Nielsen
and
I. L. Chuang,
Quantum
Computation
and
Quantum
Information,
Cambridge
University
Press
(2000).

J. Preskill’s
Lecture
Notes
on
Quantum
Information
http://www.theory.caltech.edu/people/preskill/ph229/

B.
Schumacher
and
M.
D.
Westmoreland,
Quantum
Processes,
Systems
and
Information,
Cambridge
University
Press
(2010).
PHY645: Topics in quantum physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Classical
limit
of
Quantum
mechanics:
Semiclassical
quantization,
WKB.
Coherent
states
as
“best
approximants”
to
classical
behaviour.
Squeezed
states.
This
topic
will
explore
solutions
of
the
Schroedinger
equation
using
approximate
methods,
mainly
based
on
the
saddle
point
method.
Relationships
to
BohrSommerfeld
methods
and
to
the
path
integral
will
lead
to
approximate
wavefunctions,
energy
levels,
and
to
classical
mechanics.

Perturbation
theory:
time
dependent
and
independent,
Standard
material
including
degenerate
cases.
Borel
resummation,
Diagrammatics,
Fermi
golden
rule
Non
perturbative
effects.
Instantons.

Quantum
systems
in
classical
fields:
AharonovBohm,
Landau
levels
etc.
Studying
quantum
systems
coupled
to
classical
electric
and
magnetic
fields.
Phases
in
quantum
mechanics.
Hall
effect,
Hofstadter
problem.
Problems
with
Semiclassical
theory
of
radiation
(BohrRosenfeld
analysis).

Scattering
theory:
1d,
2d
and
3d.
Poles
of
the
scattering
matrix.
Analyticity
properties.
Reference:
e.g.,
Sakurai

Symmetry
in
Quantum
mechanics:
Ordinary
and
supersymmetry.
Conserved
quantum
numbers.
Degeneracy
and
splitting.
WignerEckart
theorem
Representations
of
symmetry
groups.
Galilean
invariance
in
quantum
mechanics

Matrix
Quantum
Mechanics
(and
quantum
gravity):
This
topic
will
explore
the
quantum
mechanics
of
systems
with
large
numbers
of
degrees
of
freedom.
Large
N
limit,
Nuclear
energy
levels,
ThomasFermi
model,
and
a
relation
to
quantum
gravity
are
possible
sidelights.

Quantum
Light:
Quantum
description
of
optical
fields.
classical
and
nonclassical
light.
Photon
statistics,
subPoisson
light,
squeezed
light.
Recommended Reading

J. J. Sakurai,
Modern
Quantum
Mechanics,
Addison
Wesley
(1993).

S. Coleman,
Aspects
of
symmetry:
Selected
Erice
lectures,
Cambridge
University
Press
(1988).

L. Mandel
and
E. Wolf,
Optical
Coherence
and
Quantum
Optics,
Cambridge
University
Press
(1995).
PHY647: Basic atomic collisions and spectroscopy


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Summary:
The
course
will
cover
basic
theory
of
atomic
structure,
spectroscopy
and
collisions
and
related
experimental
techniques.
I
would
like
to
stress
more
on
the
experimental
techniques,
if
the
students
are
able
to
spend
some
time
in
laboratories
doing
such
work.
Possibilities
of
visits
are
to
the
Accelerator
at
Panjab
University,
Chandigarh
and
InterUniversity
Accelerator
Centre,
Delhi.
I
haven’t
explored
these
yet,
but
would
like
to.
The
feasibility
of
such
an
arrangement
will
depend
on
the
number
of
students.

Rutherford
Scattering,
Concept
of
crosssection
Quantum
Mechanical
Scattering
Theory
Information
expected
from
studying
of
IonAtom
Collisions

Experimental
Techniques
for
measuring
scattering
crosssections
Generation
of
charged
particle
beams
and
neutral
beams
Techniques
for
detecting
charged
and
neutral
particles
and
photons

Theory
of
atomic
spectra,
fine
structure.
Information
expected
from
studying
atomic
spectra.

Experimental
techniques
for
spectroscopy
Lineshape,
absoprtion,
emission
Optical
spectrographs
Methods
of
excitation.
Recommended Reading

B. H. Bransden
and
C. J. Joachain,
Physics
of
Atoms
and
Molecules,
Longman
Publishing
Group
(1982).

H. E. White,
Atomic
Spectra,
McGraw
Hill
(1934).

M. R. C. McDowell,
Introduction
to
the
theory
of
ionatom
collisions,
NorthHolland
Publishing
(1970).

J. A. R. Samson,
Techniques
of
Vacuum
Ultraviolet
Spectroscopy,
V
U
V
Associates
(1990).

J. M. Hollas,
Modern
Spectroscopy,
Wiley
(2004).

W. Demtroder,
Laser
Spectroscopy,
Springer
(2008).
PHY648: Lasers, devices and applications


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Course Outline

Introductory
Concepts:
Laser
Idea,
Pumping
schemes,
Properties
of
Laser
beams,
Light
in
cavities,
Essential
operating
principles
of
laser.

Interaction
of
Radiation
with
matter:
Einstein
coefficients,
light
amplification,
threshold
conditions,
Line
broadening
mechanisms.

Laser
Rate
equations:
Two/
three/
four
level
systems,
Laser
cavities
&
Modes,
Plane
&
spherical
resonators,
Mode
selection

Lasers:
HeNe/
Ar+/
CdSe/
N2/
CO2/
Nd:YAG/
Nd:
Glass/
Semiconductor/

Dye
and
Ti:sapphire
lasers.
Pulsed
lasers:
Qswitching,
Mode
locking,
Nano/
Pico/
femto
second
lasers.

Nonlinear
processes:
Propagation
of
e
m
waves
in
nonlinear
optical
media,
Parametric
mixing,
Second
harmonics,
Phase
matching,
Four
wave
mixing,
Stimulated
Raman
scattering,
Antistoke
scattering,
Optical
Kerr
Effect,
Pockel
effect.

Applications:
Laser
induced
fusion,
Light
wave
communication,
Applications
of
lasers
in
Science/
Industry/
Medicines/
FROG,
SHGFROG,
FROG
CRAB.
Recommended Reading

Thyagarajan
and
Ghatak,
Lasers–Fundamentals
and
Applications
2nd
Edn.
Springer

Orazio
Svelto
Principles
of
Laser
5th
Edn.
Springer.

B
B
Laud,
Lasers
&
Nonlinear
Optics,
Wiley
Eastern,
(1985)
PHY649: Advanced experiments in physics: Lasers and optics


[Cr:4,
Lc:0,
Tt:0,
Lb:12]
Course Outline
This elective course aims to provide hands on training and exposure to the
forefront of laser Physics and optical technology. The emphasis would be to
assemble few thought provoking experiments from scratch on an opticaltable.
Indulging into some openended experimentation and original thinking would be
encouraged.
One would learn nuts and bolts of various available lasers, including the Femtosecond
laser system. Coherent manipulation of light by various (bio)photonic crystal and
optomechanics of fluid interfaces by radiation pressure shall be covered among other
relevant topics.
Suggested modules

Basics
of
laser
operation
and
working

Training
session
with
femtosecond
lasers

Deformation
of
fluid
interfaces
by
radiation
pressure
of
a
laser
beam

Understanding
and
characterization
of
Photonic
crystals

Interferometric
techniques
for
thinfilm
characterizations

Laser
safety
and
radiation
hazard

Optical
spectroscopy
of
various
light
sources
Suggested reading

A.
E.
Sigman,
Lasers,
University
Science
Books,
1986.

A.
Ghatak,
Optics
McGrawHill,
2008.
PHY650: Ultra low temperature physics


[Cr:4,
Lc:2,
Tt:0,
Lb:10]
Course outline
The course will have lecture components that introduce both experimental and
theoretical ideas in low temperature physics. The remaining hours will involve
hands on experience in designing and experiments in the ultra low temperature
laboratory.
Review of laws of thermodynamics

liquefaction
of
helium
and
properties
of
liquid
helium
including
phenomena
like
superfluidity
,
second
sound,
phenomenological
two
fluid
theories.
Landau
theory
of
quasiparticles,
vortices
and
quantization
of
circulation

Properties
of
Helium
3
and
Helium3
helium
4
mixtures

Solid
state
systems
below
4.2K
(
mainly
acoustic
,
thermal
and
electronic
properties
)

Overview
of
topics
like
superconductivity
spin
glasses

Tehcniques
below
4.2K
,
Adiabatic
demagnetization
,
principles
of
helium3
helium
4
refrigeration,
nuclear
demagnetization
techniques
to
reach
temperatures
below
1mK

Electronics
and
instrumentation
below
4.2K
examples
like
discovery
of
cosmic
microwave
background
(CMB)
using
cryogenic
amplifiers

Low
temperature
thermometry
including
modern
techniques
like
coulomb
blockade
primary
thermometry

Modern
cryofree
techniques
to
reach
below
10
K
.
Recommended reading

C.
Enss
&
S.
Hunklinger,
Low
temperature
Physics,
Springer
(2005)

G.K.
White
&
P.
Meeson
Experimental
Techniques
in
low
temperature
physics
Oxford
(2002)

D.S.
Betts
An
Introduction
to
Millikelvin
Technology
Cambridge
(1989)
PHY652: Phase transition and critical phenomena


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
thermodynamics
and
equilibrium
Statistical
Mechanics.
Partition
function
for
interacting
system,
virial
expansion.
Zeros
of
the
partition
function.

Ising
model,
mean
eld
theory,
Brag
Williams
approximation.
Equivalence
of
Ising
model
to
other
models,
Spontaneous
magnetization,
Solution
of
Ising
model
using
transfer
matrix,
high
and
low
temperature
expansions
and
Monte
Carlo
simulations.

Order
parameter,
correlation
function,
critical
exponents,
scaling
hypothesis,
importance
of
dimensionality.
Landau
free
energy,
LandauGinzburg
mean
eld
theory,
Functional
integration,
Gaussian
model.

Renormalization
group
transformations,
xed
points,
real
and
momentum
space
renormalization.

Nonlinear
model,
XY
model,
Two
dimensional
solids
and
melting
(KosterlitzThouless
transition).
Recommended Reading

Kerson
Huang,
Statistical
Mechanics,
Second
Ed.
John
Wiley
Sons,
Singapore
2000.

R.
K.
Pathria,Statistical
Mechanics,
Second
Ed.
ButterworthHeineman
Oxford
1996.

N.
Goldenfeld,
Lectures
on
Phase
Transitions
and
the
Renormalization
Group,
Levant
Books,
Kolkata
2005.

J.
J.
Binney,
N.
J.
Dowrick,
A.
J.
Fisher
&
M.
E.
J.
Newman,The
theory
of
Critical
Phenomena,
Oxford
2002.

J.
M.
Yeomans,
Statistical
Mechanics
of
Phase
Transitions,
Oxford
1997.
PHY653: Physics of polymers


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline
Introduction to polymers, coarsegraining in polymers. Brownian motion and
stochastic processes, OrnsteinUhlenbeck process, FluctuationDissipation theorem,
Correlation and response functions,FokkerPlanck and Smoluchowski equation and its
application. Interacting Brownian particleshydrodynamic interactions and its
origin. Review of equilibrium statistical mechanicscanonical and microcanonical
ensembles.

Statics
of
single
chain
polymers
end
to
end
distance,
distribution
of
end
to
end
distance
in
models
of
polymer
(freely
jointed
chain,
freely
rotating
chain,
Wormlike
chain
model
and
Gaussian
chain).

Dynamics
of
single
chain
Rouse
model,
Zimm
model,
density
modes
and
dynamical
scaling.
Viscoelasticity
origin
of
viscoelasticity,
constitutive
relations,
microscopic
stress
tensor.

Statics
and
Dynamics
of
many
chain
systems:
Thermodynamics
of
mixing
Entropy
and
free
energy
of
mixing,
FloryHuggins
theory,
classi
cation
of
good
and
poor
solvents,
Gaussian
approximation
to
concentration
uctuation,
scaling
theory
statics.

Dynamics
of
the
density
modes
wavevector
dependent
relaxation
times.
scaling
theory
dynamics.

Rod
like
polymers:
rotational
and
translational
di
usion.
Dynamic
light
scattering
of
rod
like
polymers.
Onsager
theory
of
phase
transition
isotropic
and
nematic
order.

Experimental
tools
in
polymer
physics
intermediate
scattering
functions,
static
and
dynamic
structure
factors.
Recommended Reading

M.
Rubinstein
&
Ralph
H.
Colby.,
Polymer
Physics
(Chemistry),
Oxford
University
Press,
USA,
1
edition,
6
2003.

PierreGilles
de
Gennes,
Introduction
to
Polymer
Dynamics
(Lezioni
Lincee),
Cambridge
University
Press,
9
1990.

M.
Doi
&
S.
F.
Edwards.
The
Theory
of
Polymer
Dynamics
(Monographs
on
Physics),
Oxford
University
Press,
USA,
12
1986.

PierreGilles
Gennes,
Scaling
Concepts
in
Polymer
Physics.,
Cornell
University
Press,
1
edition,
11
1979.

Crispin
Gardiner,
Stochastic
Methods:
A
Handbook
for
the
Natural
and
Social
Sciences
(Springer
Series
in
Synergetics),
Springer,
softcover
reprint
of
hardcover
4th
ed.
2009
edition,
10
2010.

N.G.
Van
Kampen,
Stochastic
Processes
in
Physics
and
Chemistry,
Third
Edition
(NorthHolland
Personal
Library),
North
Holland,
3
edition,
5
2007.
PHY654: Cosmology and galaxy formation


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Galaxies,
types
of
galaxies,
morphological
distribution,
large
scale
distribution
of
galaxies,
clustering
of
galaxies,
large
scale
homogeneity
and
isotropy,
A
cosmic
inventory.

Hubbles
law,
expansion
of
the
universe,
comoving
coordinates.

Cosmological
principle,
FriedmanRobertsonWalkerLemaitre
model,
Cosmological
models.
Distance
redshift
relation.
Luminosity
distance
and
angular
diameter
distance.
Measurement
of
Hubbles
constant,
age
of
the
universe,
distance
measurements
and
estimation
of
cosmological
parameters.
Accelerated
expansion.

Newtonian
limit,
nonrelativistic
perturbation
theory,
growth
of
perturbations
in
the
linear
limit.
Nonlinear
growth
of
perturbations.
NBody
simulations.

Dark
matter
halos,
universal
density
profiles.

Theory
of
mass
functions,
excursion
sets,
merger
rates
for
halos.

Formation
of
galaxies,
feedback
from
star
formation
and
evolution
of
galaxies.
Super
massive
black
holes
and
active
galactic
nuclei.
Comparison
of
models
with
observations.

Clusters
of
galaxies,
intracluster
medium,
SunyaevZeldovich
effect.

History
of
the
universe:
the
dark
ages,
formation
of
first
galaxies,
reionization,
evolution
of
the
inter
galactic
medium.
Revisiting
the
cosmic
inventory.
Recommended Reading

Large
Scale
Structure
of
the
Universe,
P.
J.
E.
Peebles,
Princeton
Series
in
Physics,
Princeton
University
Press,
1980.

Principles
of
Physical
Cosmology,
P.
J.
E.
Peebles,
Princeton
Series
in
Physics,
Princeton
Uni
versity
Press,
1993.

Structure
Formation
in
the
Universe,
T.
Padmanabhan,
Cambridge
University
Press,
1993.

Theoretical
Astrophysics,
Vol.III:
Galaxies
and
Cosmology,
T.
Padmanabhan,
Cambridge
University
Press,
2002.

Galaxy
Formation,
Malcolm
S.
Longair,
Astronomy
and
Astrophysics
Library,
Springer,
2000.

Cosmology,
S.
Weinberg,
Oxford
University
Press,
2008.

Gravitation
and
Cosmology,
S.
Weinberg,
Wiley.

Galaxy
Formation
and
Evolution,
Houjun
Mo,
Frank
van
den
Bosch
and
Simon
White,
Cambridge
University
Press,
2010.

Cosmological
Physics,
J.
A.
Peacock,
Cambridge
Astrophysics,
Cambridge
University
Press,
1998.
PHY655: Special topics in particle physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Overview
of
Particle
Physics,
including
major
historical
and
latest
developments.

Introduction
to
Relativistic
Quantum
Mechanics
and
Quantum
Field
Theory.

Relativistic
Kinematics
and
Phase
Space:
Introduction
to
relativistic
kinematics,
particle
reactions,
Lorentz
invariant
phase
space,
twobody
and
three
body
phase
space
etc.

Invariance
principles
and
Conservation
Laws:
Invariance
in
classical
mechanics
and
in
quantum
mechanics,
parity,
charge
conjugation,
time
reversal
invariance,
CPT
theorem,
O(3),
SU(2),
SU(3),
quark
model
etc.

Abelian
and
NonAbelian
gauge
transformations:
Construction
of
lAbelian
and
NonAbelian
gauge
invariant
lagrangians.
Spontaneous
symmetry
breaking.
Spontaneous
symmetry
breaking
of
a
gauge
theory.

Standard
Model
of
Particle
Physics:
formulation
of
VA
theory
of
weak
interactions.
Electroweak
unification.SU(3)X
SU(2)X
U(1)
gauge
theory
etc.

Beyond
the
standard
model:
Flavor
mixings,
mass
matrices.
CKM
and
PMNS
matrices.
CP
violation
etc.
Grand
Unified
theories.
Recommended Reading

An
introduction
to
High
Energy
Physics,
D.H.
Perkins,
Cambridge
Press
4th
ed.2000.

Introduction
to
Quarks
and
Partrons,
F.E.
Close,
Academic
Press,
London,
1979.

Gauge
Theories
of
Weak,
Strong
and
Electromagnetic
Interactions,
C.
Quigg,
AddisonWesley,
1994.

First
book
of
Quantum
Field
Theory,
A.
Lahiri
and
P.
Pal,
Narosa,
New
Delhi.
2nd
ed.
2007.
PHY656: Quantum principles and quantum optics


[Cr:3,
Lc:3,
Tt:0,
Lb:0]
Course Outline

Introduction
to
fundamental
principles
of
quantum
mechanics,
quantum
superposition,
quantum
entanglement,
EPR
paradox.
Quantization
of
electromagnetic
field,
concept
of
photon,
vacuum
field,
zero
point
energy,
Casimir
effect,
coherent
states
of
light,
squeezed
states,
phase
space
representation
of
quantum
states
of
light,
classical
analogy
of
a
coherent
state.

Beam
splitter
quantum
mechanics,
first
and
second
order
interference,
MandelOu
effect,
HanburyBrownTwiss
(HBT)
effect,
HBT
effect
for
classical
and
quantum
light,
photIntroduction
to
fundamental
principles
of
quantum
mechanics,
quantum
superposition,
quantum
entanglement,
EPR
paradox.
Quantization
of
electromagnetic
field,
concept
of
photon,
vacuum
field,
zero
point
energy,
Casimir
effect,
coherent
states
of
light,
squeezed
states,
phase
space
representation
of
quantum
states
of
light,
classical
analogy
of
a
coherent
state.
Beam
splitter
quantum
mechanics,
first
and
second
order
interference,
MandelOu
effect,
HanburyBrownTwiss
(HBT)
effect,
HBT
effect
for
classical
and
quantum
light,
photon
bunching
and
antibunching,
higher
order
coherence.
Single
photon
interference
experiments,
typeI
and
type
II
down
conversion,
generation
of
entangledphotons,
polarization
entangled
photons,
experiments
based
on
entangled
photons,
quantum
erasure,
wheeler
s
delayed
choice
thought
experiment,
delayed
choice
quantum
erasure.
Atomlight
interaction,
semiclassical
model,
population
oscillations,
quantum
model
of
atomphotoninteraction,
collapse
and
revival
of
population,
dressed
state
picture
of
atomlight
interaction,
atomphoton
entanglement.
Introduction
to
laser
cooling,
optical
molasses,
magneto
optical
trap,
sisyphus
cooling,
trapping
ofneutral
atoms,
evaporative
cooling,
Bose
Einstein
condensation.
on
bunching
and
antibunching,
higher
order
coherence.

Single
photon
interference
experiments,
typeI
and
type
II
down
conversion,
generation
of
entangledphotons,
polarization
entangled
photons,
experiments
based
on
entangled
photons,
quantum
erasure,

wheeler
s
delayed
choice
thought
experiment,
delayed
choice
quantum
erasure.

Atomlight
interaction,
semiclassical
model,
population
oscillations,
quantum
model
of
atomphotoninteraction,
collapse
and
revival
of
population,
dressed
state
picture
of
atomlight
interaction,
atomphoton
entanglement.

Introduction
to
laser
cooling,
optical
molasses,
magneto
optical
trap,
sisyphus
cooling,
trapping
ofneutral
atoms,
evaporative
cooling,
Bose
Einstein
condensation.
Recommended Reading

J.
J.
Sakurai,
Modern
Quantum
Mechanics,
Pearson
Education,
Inc.

C.
Gerry,
P.
Knight,Introductory
Quantum
Optics,
Cambridge
University
Press.

M.
O.
Scully
&
M.
S.
Zubairy,
Quantum
Optics,
Cambridge
University
Press.

D.
Bouwmeester,
A.
Ekert
&
A.
Zeilinger
(Eds),
The
Physics
of
Quantum
Information
PHY657: Radiofrequency and microwave circuits


[Cr:4,
Lc:3,
Tt:0,
Lb:3]
Course Outline

This
course
will
emphasize
importance
of
radiofrequency
and
microwave
circuits
in
modern
physical
experiments
ranging
from
applications
like
fast
circuits
in
quantum
computing
or
measuring
the
cosmic
microwave
background.

Review
of
Maxwells
equations
and
basic
electrodynamics,
lumped
versus
distributed
circuit
elements
Basics
of
transmission
lines
Wave
guides,
analysis
of
microwave
networks
using
Smatrix
parameters,
smith
chart,
impedance
matching
tuning
,
passive
components
like
attenuators,
directional
couplers
,
magicTee,
phase
shifters
bias
tee,
microwave
resonators
and
planar
circuits
like
microstrips,
coplanar
waveguides.
Active
components
like
low
noise
amplifiers
and
basics
of
microwave
ICs.
Mixers
,
low
noise
amplifiers
,
basics
of
microwave
synthesizers
.

Additional
topics
:
Analogy
between
theory
of
transmission
lines
and
simple
tunneling
in
quantum
mechanics,
applications
to
physical
systems.
Microwave
instruments
like
radars.
Basics
of
test
equipment
like
network
analyzer,
RF
lockin
amplifier
.
Detailed
study
of
applications
of
Microwave
or
RF
circuits
in
selected
modern
physics
experiments
e.g.
cyclotron
resonance
of
carriers
in
semiconductors,
Nuclear
magnetic
resonance,
radio
astronomy,
rotational
spectra
of
molecules
using
microwave
spectroscopy
etc.

Laboratory
work
involves
designing,
construction
and
testing
of
few
components.
Recommended Reading

R.E.
Collin,
Foundations
of
Microwave
Engineering,
2nd
Edition
Wiley
(2001).

D.M.
Pozar,
Microwave
Engineering,
4th
Edition
,
Wiley
(2011).

F.E.
Terman,
Electronic
&
Radio
Engineering,
McGraw
Hill
(1955).

J.A.
Stratton,
Electromagnetic
Theory,
Mc
Graw
Hill
(1941).

Feynman
et.al,
Feynman
Lectures
Volume
II,
Addison
Wesley
(1964).

L.
Brilloin,
Wave
propagation
in
periodic
structures,
McGraw
Hill
(1946).

R.
Teppati
et.al,
Modern
RF
and
Microwave
Measurement
Techniques,
(The
Cambridge
RF
and
Microwave
Engineering
Series),
Cambridge
University
Press
(2013).
PHY658: Radiative effects and renormalization group in relativistic quantum field
theory


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Course Outline

Survey
of
Kinematics
and
Cross
section
formulae
for
Elementary
Processes.
Tree
level
calculation
of
Feynman
amplitudes
and
cross
sections
for
Yukawa
coupled
FermionScalar
Theory
(FST)
and
QED.

Radiative
corrections:
Brehmstrahlung,
Vertex
functions,
Summation
and
interpretation
of
Infrared
divergences.

Loop
Calculations,
UV
divergences
and
Systematics
of
Renormalization:
One
loop
structure
of
Phi4
theory,
FermionScalar
theory
(FST)
and
QED.
Renormalization
program.
Regularization,
Counter
terms
and
WardTakahashi
identities.
Cancellation
of
Infrared
Divergences.

Renormalization
Group:
Callan
Symanzik
equation.
Evolution
of
coupling
constants,
scale
factors
and
mass
parameters.
Asymptotic
freedom.
Coleman
Weinberg
potential.
Applications
of
RG
to
Unified
theories.

Functional
methods.
Functional
quantization
of
scalar
and
spinor
fields.
QED.
Symmetries
in
Functional
formalism.

Renormalization
and
Symmetry:
Spontaneous
symmetry
breaking
and
linear
Sigma
model.
Effective
action
and
its
computation.
Symmetry
breaking
and
linear
Sigma
model.
Recommended Reading

M.
E.
Peskin
&
D.
V.
Schroeder,
An
Introduction
to
Quantum
Field
Theory,
Addison
Wesley
(1995).

A.
Lahiri
&
P.B.
Pal,
A
First
book
of
Quantum
Field
Theory,
Narosa/Springer
(2001).

T.P.Cheng
&
L.F.
Li,
Gauge
Theory
of
Elementary
Particle
Physics,
Oxford
(2000).
PHY659: Gauge theories, the standard model and beyond


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Course Outline

Symmetries
and
Symmetry
Breaking
in
QFT.
Continuous
groups:
Lorentz
group
SO(1,3)
and
its
representations.
Dirac,
Weyl
and
Majorana
fermions.
Unitary
groups
and
Orthogonal
groupsand
their
representations.
Discrete
symmetries
:
Parity,
Charge
Conjugation
and
Time
reversal
Invariance,
CP,CPT.

Global
and
Local
invariances
of
the
Action.
Approximate
symmetries.
Noethers
theorem.
Spontaneous
breaking
of
symmetry
and
Goldstone
theorem.
Higgs
mechanism.

Abelian
and
NonAbelian
gauge
fields.
Lagrangian
and
gauge
invariant
coupling
to
matter
fields.

Standard
Model
of
Particle
Physics
:
SU(3)
x
SU(2)
x
U(1)
gauge
theory,
Coupling
to
Higgs
and
Matter
fields
of
3
generations.
Gauge
boson
and
fermion
mass
generation
via
spontaneous
symmetry
breaking,
CKM
matrix
.
Low
energy
Electroweak
effective
theory
and
Decoupling.
Elementary
electroweak
scattering
processes.

QCD
and
quark
model:
Asymptotic
freedom
and
Infrared
slavery
,
confinement
hypothesis.
Approximate
flavor
symmetries
of
the
QCD
lagrangian.
Classification
of
hadrons
by
flavor
symmetry
:
SU(2)
and
SU(3)
multiplets
of
Mesons
and
Baryons.
Chiral
symmetry
and
chiral
symmetry
breaking,
Sigma
model.
Parton
model
and
Deep
inelastic
scattering
structure
functions.
Optional advanced topics

Path
Integrals
and
Functional
Quantization:
Path
integrals
in
QM,
Functional
quantization
of
scalar
and
spin
1/2
fields.
Functional
Quantization
of
Gauge
theories.
Feynman
rules
for
gauge
theories
.
Symmetries
in
the
functional
formalism.
The
effective
action
and
its
computation.

Beyond
The
Standard
Model:
Neutrino
mass
and
neutrino
oscillations.
Models
of
Neutrino
mass.
Left
Right
symmetric
models.
PatiSalam,
SU(5)
and
SO(10)
Grand
Unification.
Unification
of
gauge
and
Yukawa
couplings
via
RG
flows.
Supersymmetry
and
Supersymmetric
Unification.
Exotic
processes
and
their
phenomenology.
Higgs
Physics.
Collidar
Physics.
Dark
matter.
Baryon
asymmetry
generation.
Leptogenesis.
Recommended Reading

Gauge
Theory
of
Elementary
Particle
Physics,
T.P
Cheng
&
L.F.
Li
(Oxford).

An
Introductory
Course
of
Particle
Physics,
Palash
Pal
(CRC
Press).

First
Book
of
Quantum
Field
Theory,
A.
Lahiri
&
P.
Pal
,
Narosa,
New
Delhi.

Introduction
to
Quantum
Field
Theory,
M.
Peskin
&
D.V.
Schroeder.
(Levant
Books).

Dynamics
of
the
Standard
Model,
J.F.
Donoghue
(Cambride
University
Press).
PHY660: Nonlinear optics


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Course Outline

Introduction
to
anisotropic
media,
double
refraction,
wave
propagation
in
anisotropic
medium,
applications
of
index
ellipsoid,
energy
and
momentum
of
light
field
in
anisotropic
media,
wave
plates,
physics
of
polarization
controlling
devices,
electrooptic
modulators.

Concepts
of
nonlinear
phenomena,
nonlinear
electric
polarizability,
second
order
nonlinear
processes;
second
harmonic
generation,
conceptual
description
of
phase
matching,
parametric
up
and
down
conversion,
parametric
oscillators
and
amplifiers,
entangled
photon
generation.

Third
order
nonlinear
processes;
third
harmonic
generation,
optical
Kerr
effect,
self
focusing,
self
phase
modulation,
supercontinuum
generation,
cross
phase
modulation,
four
wave
mixing,
optical
phase
conjugation
and
its
applications.

Nonlinear
optical
effects
in
optical
waveguides
and
optical
fibers,
applications
of
nonlinear
optics
in
quantum
optics
experiments,
nonlinear
effects
in
BoseEinstein
condensation,
higher
order
nonlinear
effects.
Recommended Reading

The
Principles
of
Nonlinear
Optics,
Y.
R.
Shen,
John
Wiley
and
Sons
Inc
(2003).

Nonlinear
Optics,
Robert
Boyd,
Elsevier
Inc
(2008).

Nonlinear
Fiber
Optics,
G.
P.
Agrawal,
Elsevier
Inc
(2013).
PHY661: Selected topics in classical and quantum mechanics


[Cr:4,
Lc:3,
Tt:0,
Lb:0]
Course Outline

Group
theory
and
symmetry
in
physics.

Symplectic
groups
and
their
uses
in
physics,
uncertainty
relations.

Geometric
Phases
in
physics.

Classical
theory
of
constrained
systems.

Quantum
Theory
of
Angular
Momentum.

Theory
of
Wigner
distributions.

The
Wigner
theory
of
UIRs
of
the
Poincare
group.

Dissipative
quantum
mechanics.
Recommended Reading

Lectures
on
Advanced
Mathematical
Methods
for
Physicists,
Sunil
Mukhi
and
N.
Mukunda,
World
Scientific
(2010).

Symplectic
Techniques
in
Physics,
V.
Guillemin
and
S.
Sternberg,
Cambridge
University
Press
(1990).

Angular
Momentum
in
Quantum
Mechanics,
A.
R.
Edmonds,
Princeton
University
Press
(1996).

Decoherence
and
the
QuantumtoClassical
Transition,
M.
A.
Schlosshauer,
Springer
(2008).

Geometric
Phases
in
Physics,
Advanced
Series
in
Mathematical
Physics
Volume
5,
Edited
by
F.
Wilczek
and
A.
Shapere,
World
Scientific
(1989).

Constrained
Dynamics:
With
Applications
to
YangMills
Theory,
General
Relativity,
Classical
Spin,
Dual
String
Model:
Lecture
Notes
in
Physics,
Kurt
Sundermeyer,
SpringerVerlag
(1982).

Distribution
Functions
in
Physics:
Fundamentals,
M.
Hillery,
R.
F.
OConnell,
M.
O.
Scully
and
E.
P.
Wigner,
Physics
Reports,
106,
pp121167
(1984).
PHY662: Statistical physics of fields


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Collective
Behavior,
from
particles
to
fields
:
Introduction,
Phonons
&
elasticity,
Phase
transitions,
Critical
Behavior.

Statistical
Fields
:
Introduction,
The
LandauGinzburg
Hamiltonian,
Saddle
point
approximation
and
mean
field
theory,
Continuous
symmetry
breaking
and
Goldstone
modes,
Discrete
symmetry
breaking
and
domain
walls.

Fluctuations
:
Scattering
and
fluctuations,
Correlation
functions
and
susceptibilities,
Lower
critical
dimension,
Comparison
to
experiments,
Gaussian
integrals,
Fluctuation
corrections
to
the
saddle
point,
The
Ginzburg
criterion.

The
scaling
hypothesis
:
The
homogeneity
assumption,
Divergence
of
correlation
length,
Critical
correlation
functions
and
self
similarity,
The
renormalization
group
(conceptual),
The
renormalization
group
(formal),
The
Guassian
model
(direct
solution),
The
Gaussian
model
(renormalization
group).

Perturbative
renormalization
group
:
Expectation
values
in
the
Gaussian
model,
Expectation
values
in
perturbation
theory,
Diagrammatic
representation
of
perturbation
theory,
Susceptibility,
Perturbative
RG
(first
order),
Perturbative
RG
(second
order),
The
epsilon
expansion,
Irrelevance
of
other
interactions,
Comments
on
the
epsilon
expansion.

Lattice
systems
:
Models
and
methods,
Transfer
matrices,
Position
space
RG
in
one
dimension,
The
NiemeijervanLeeuwen
cumulant
approximation,
The
MigdalKadanoff
bond
moving
approximation,
Monte
Carlo
simulations.

Series
expansions
:
Low
temperature
expansions,
High
temperature
expansions,
Exact
solution
of
the
one
dimensional
Ising
model,
Self
duality
in
the
twodimensional
Ising
model,
Dual
of
the
three
dimensional
Ising
model,
Summing
over
phantom
loops,
Exact
free
energy
of
the
square
lattice
Ising
model,
Critical
behavior
of
the
twodimensional
Ising
model.

Beyond
spin
waves
:
The
nonlinear
sigma
model,
Topological
defects
in
the
XY
model,
Renormalization
group
for
the
Coulomb
gas,
Twodimensional
solids,
Twodimensional
melting.

Dissipative
dynamics
:
Brownian
motion
of
a
particle,
Equilibrium
dynamics
of
a
field,
Dynamics
of
a
conserved
field,
Generic
scale
invariance
in
equilibrium
systems,
Nonequilibrium
dynamics
of
open
systems,
Dynamics
of
a
growing
surface.
Recommended Reading

Mehran
Kardar,Statistical
Physics
of
Fields.

P.
M.
Chaikin
&
T.
C.
Lubensky,
Principles
of
condensed
matter
physics.
PHY663: Relativistic cosmology and the early universe


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Expansion
of
the
Universe,
FriedmanRobertsonWalkerLemaitre
model,
Geodesics
and
Distance,
geodesic
deviation,
Standard
candles
and
Standard
Rulers.

Standard
cosmological
model:
radiation
dominated
era,
matter
domination,
dark
energy
and
accelerated
expansion.
Horizon
problem,
flatness
problem.
Inflationary
paradigm.

Thermal
history
of
the
universe,
primordial
nucleosynthesis,
decoupling
of
neutrinos,
weakly
interact
ing
massive
particles,
electronpositron
annihilation,
matter
radiation
decoupling,
last
scattering
surface,
cosmic
microwave
background
radiation.

Scalar
fields
in
an
expanding
universe.
Generation
of
perturbations
in
inflation,
Tensor
and
Scalar
per
turbations,
Reheating.

Perturbations
in
an
expanding
universe.
relativistic
perturbation
theory,
growth
of
perturbations
in
dif
ferent
scenarios.
Fluctuations
in
the
cosmic
microwave
background
radiation.
Transfer
Functions,
Baryon
Acoustic
oscillations,

SachsWolfe
and
Integrated
Sachs
Wolfe
effect,
Silk
damping,
The
observed
fluctuations
in
the
cosmic
microwave
background
radiation
and
its
relation
with
Cosmological
Parameters,
Observational
constraints.

Late
time
perturbations,
geometric
effects,
redshift
space
distortions.
Recommended Reading

T.
Padmanabhan,
Theoretical
Astrophysics,
Vol.III:
Galaxies
and
Cosmology,
Cambridge
University
Press,
2002.

S.
Weinberg,
Cosmology,
Oxford
University
Press,
2008.

Ruth
Durrer,
The
cosmic
microwave
background,
Cambridge
University
Press,
2008.

Scott
Dodelson,
Modern
Cosmology,Elsevier,
2005.
PHY664: Quantum Thermodynamics


[Cr:4,
Lc:3,
Tt:0,
Lb:0]
Course Outline

Review
of
Thermodynamics:
laws
of
thermodynamics,
thermodynamic
potentials,
work
extraction
processes,
entropy
and
information,
Maxwell’s
demon,
Landauer
principle.

Review
of
quantum
mechanics:
density
matrix
formalism,
composite
quantum
systems,
reduced
density
matrix,
entanglement,
purity,
quantum
entropy,
relative
entropy,
quantum
measurements.

Quantum
thermodynamic
machines:
heat
cycles,
quantum
thermodynamic
processes,
quantum
adiabatic
theorem,
thermal
efficiency,
effect
of
interacting
working
medium,
quantum
friction,
quantum
Maxwell’s
demon.

Time
evolution.
Liouvillevon
Neumann
equation,
Heisenberg
and
interaction
picture,
Markovian
quantum
master
equation,
Lindblad
operators,
weak
coupling
limit,
relaxation
to
equilibrium,
decay
of
twolevel
system,
coherence
enhanced
efficiency
of
quantum
heat
engine.
Recommended Reading

J.
Gemmer,
M.
Michel,
G.
Mahler
Quantum
Thermodynamics:
Emergence
of
Thermodynamic
Behavior
Within
Composite
Quantum
Systems,
Lecture
Notes
in
Physics,
Springer
(2009).

G.
Mahler,
Quantum
Thermodynamic
Processes:
Energy
and
Information
Flow
at
the
Nanoscale,
Pan
Stanford
(2014).

H.
P.
Breuer
and
F.
Petruccine,Theory
of
Open
Quantum
Systems,
Clarendon
Press,
Oxford
(2002).