Semester I | Semester II |

PS 415 Physics Laboratory I (6 credits) | PS 427 Computational Physics (3 credits) |

Semester III | Semester IV |

PS 512 Subatomic Physics (3 credits) | PS 522 Project (4 credits) |

PS 513 Statistical Mechanics II (3 credits) | Electives * |

PS 514 Atoms and Molecules (3 credits) | PS 523 Astrophysics, Gravitation and Cosmology (3 credits) |

PS 515 Physics Laboratory III (6 credits) | PS 524 Quantum Field Theory (3 credits) |

PS 525 Biophysics (3 credits) | |

PS 526 Laser Physics (3 credits) | |

PS 527 Advanced Condensed Matter Physics (3 credits) | |

PS 528 Nonlinear Dynamics (3 credits) |

1. Matrices

Linear vector spaces, matrix spaces, linear operators, eigenvectors and eigenvalues, matrix diagonalization, special matrices.

2. Group Theory

Symmetries and groups, multiplication table and representations, permutation group, translation and rotation groups, O(N) and U(N) groups.

3. Complex Analysis

Analytic functions, Cauchy-Riemann conditions, classification of singularities, Cauchy's theorem, Taylor and Laurent expansions, analytic continuation, residue theorem, evaluation of definite integrals, summation of series, gamma function, zeta function, method of steepest descent.

4. Ordinary Differential Equations and Special Functions

Linear ordinary differential equations and their singularities, series solution of second- order equations, hypergeometric and Bessel functions, classical polynomials, Sturm- Liouville problem, expansion in orthogonal functions.

References:

G.B. Arfken, Mathematical Methods for Physicists.

P. Dennery and A. Krzywicki, Mathematics for Physicists.

P.K. Chattopadhyay, Mathematical Physics.

A.W. Joshi, Matrices and Tensors in Physics.

R.V. Churchill and J.W. Brown, Complex Variables and Applications.

P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Volume I & II).

M.R. Spiegel, Complex Variables.

1. Lagrangian and Hamiltonian Formulations of Mechanics

Calculus of variations, Hamilton's principle of least action, Lagrange's equations of motion, conservation laws, systems with a single degree of freedom, rigid body dynamics, symmetrical top, Hamilton's equations of motion, phase plots, fixed points and their stabilities.

2. Two-Body Central Force Problem

Equation of motion and first integrals, classification of orbits, Kepler problem, scattering in central force field.

3. Small Oscillations

Linearization of equations of motion, free vibrations and normal coordinates, forced oscillations.

4. Special Theory of Relativity

Lorentz transformation, relativistic kinematics and dynamics, E=mc2.

5. Hamiltonian Mechanics and Chaos

Canonical transformations, Poisson brackets, Hamilton-Jacobi theory, action-angle variables, perturbation theory, integrable systems, introduction to chaotic dynamics.

References:

H. Goldstein, Classical Mechanics.

L.D. Landau and E.M. Lifshitz, Mechanics.

I.C. Percival and D. Richards, Introduction to Dynamics.

J.V. Jose and E.J. Saletan, Classical Dynamics: A Contemporary Approach.

E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies.

N.C. Rana and P.S. Joag, Classical Mechanics.

1. Introduction

Empirical basis, wave-particle duality, electron diffraction, notion of state vector and its probability interpretation.

2. Structure of Quantum Mechanics

Operators and observables, significance of eigenfunctions and eigenvalues, commutation relations, uncertainty principle, measurement in quantum theory.

3. Quantum Dynamics

Time-dependent Schrödinger equation, stationary states and their significance, time-independent Schrödinger equation.

4. One-dimensional Schrödinger Equation

Free-particle solution, wave packets, particle in a square well potential, transmission through a potential barrier, simple harmonic oscillator by wave equation and operator methods, charged particle in a uniform magnetic field, coherent states.

5. Spherically Symmetric Potentials

Separation of variables in spherical polar coordinates, orbital angular momentum, parity, spherical harmonics, free particle in spherical polar coordinates, square well potential, hydrogen atom.

References:

C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Volume I).

L.I. Schiff, Quantum Mechanics.

E. Merzbacher, Quantum Mechanics.

R.P. Feynman, Feynman Lectures on Physics (Volume 3).

A. Messiah, Quantum Mechanics (Volume I).

- R. Shankar, Principles of Quantum Mechanics.

1. G.M. Counter.

2. Experiments with microwaves.

3.Electrical resistance of a superconductor, metal and a semiconductor.

4.Work function of Tungsten, Richardson's equation.

5. Hall effect.

6.Thermal conductivity of Teflon.

7. Susceptibility of Gadolinium.

8.Transmission line, propagation of mechanical and EM waves.

9.Dielectric constant of ice.

10. Elastic properties of a solid using piezoelectric oscillator.

11. Measurement of e/m by Thomson effect.

12. Measurement of Planck's constant byphotoelectric effect.

13. Michelson interferometer.

Note: Each student is required to perform at least 8 of the above experiments.

1. Symmetry in Quantum Mechanics

Symmetry operations and unitary transformations, conservation principles, space and time translations, rotation, space inversion and time reversal, symmetry and degeneracy.

2. Angular Momentum

Rotation operators, angular momentum algebra, eigenvalues of J^{2} and J

_{z}, spinors and Pauli matrices, addition of angular momenta.

3. Identical Particles

Indistinguishability, symmetric and antisymmetric wave functions, incorporation of spin, Slater determinants, Pauli exclusion principle.

4. Time-independent Approximation Methods

Non-degenerate perturbation theory, degenerate case, Stark effect, Zeeman effect and other examples, variational methods, WKB method, tunnelling.

5. Time-dependent Problems

Schrödinger and Heisenberg picture, time-dependent perturbation theory, transition probability calculations, golden rule, adiabatic approximation, sudden approximation, beta decay as an example.

6. Scattering Theory

Differential cross-section, scattering of a wave packet, integral equation for the scattering amplitude, Born approximation, method of partial waves, low energy scattering and bound states, resonance scattering.

References:

Same as in Quantum Mechanics I plus

1. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Volume II).

2. A. Messiah, Quantum Mechanics (Volume II).

3. S. Flügge, Practical Quantum Mechanics.

4. J.J. Sakurai, Modern Quantum Mechanics.

5. K. Gottfried, Quantum Mechanics.

1. Elementary Probability Theory

Binomial, Poisson and Gaussian distributions, central limit theorem.

2. Review of Thermodynamics

Extensive and intensive variables, laws of thermodynamics, Legendre transformations and thermodynamic potentials, Maxwell relations, applications of thermodynamics to (a) ideal gas, (b) magnetic material, and (c) dielectric material.

3. Formalism of Equilibrium Statistical Mechanics

Concept of phase space, Liouville's theorem, basic postulates of statistical mechanics, ensembles: microcanonical, canonical, grand canonical, and isobaric, connection to thermodynamics, fluctuations, applications of various ensembles, equation of state for a non-ideal gas, Van der Waals' equation of state, Meyer cluster expansion, virial coefficients.

4. Quantum Statistics

Fermi-Dirac and Bose-Einstein statistics. Applications of the formalism to:

(a) Ideal Bose gas, Debye theory of specific heat, properties ofblack-body radiation, Bose- Einstein condensation, experiments on atomic BEC, BEC in a harmonic potential.

(b) Ideal Fermi gas, properties of simple metals, Pauli paramagnetism, electronic specific heat, white dwarf stars.

References:

F. Reif, Fundamentals of Statistical and Thermal Physics.

K. Huang, Statistical Mechanics.

R.K. Pathria, Statistical Mechanics.

D.A. McQuarrie, Statistical Mechanics.

S.K. Ma, Statistical Mechanics.

1. Electrostatics

Differential equation for electric field, Poisson and Laplace equations, formal solution for potential with Green's functions, boundary value problems, examples of image method and Green's function method, solutions of Laplace equation in cylindrical and spherical coordinates by orthogonal functions, dielectrics, polarization of a medium, electrostatic energy.

2. Magnetostatics

Biot-Savart law, differential equation for static magnetic field, vector potential, magnetic field from localized current distributions, examples of magnetostatic problems, Faraday's law of induction, magnetic energy of steady current distributions.

3. Maxwell's Equations

Displacement current, Maxwell's equations, vector and scalar potentials, gauge symmetry, Coulomb and Lorentz gauges, electromagnetic energy and momentum, conservation laws, inhomogeneous wave equation and Green's function solution.

4. Electromagnetic Waves

Plane waves in a dielectric medium, reflection and refraction at dielectric interfaces, frequency dispersion in dielectrics and metals, dielectric constant and anomalous dispersion, wave propagation in one dimension, group velocity, metallic wave guides, boundary conditions at metallic surfaces, propagation modes in wave guides, resonant modes in cavities.

5. Radiation

Field of a localized oscillating source, fields and radiation in dipole and quadrupole approximations, antenna, radiation by moving charges, Lienard-Wiechert potentials, total power radiated by an accelerated charge, Lorentz formula.

6. Covariant Formulation of Electrodynamics

Four-vectors relevant to electrodynamics, electromagnetic field tensor and Maxwell's equations, transformation of fields, fields of uniformly moving particles.

7. Concepts of Plasma Physics

Formation of plasma, Debye theory of screening, plasma oscillations, motion of charges in electromagnetic fields, magneto-plasma, plasma confinement, hydromagnetic waves.

References:

J.D. Jackson, Classical Electrodynamics.

D.J. Griffiths, Introduction to Electrodynamics.

J.R. Reitz, F.J. Milford and R.W. Christy, Foundations of Electromagnetic Theory.

W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetism.

F.F. Chen, Introduction to Plasma Physics and Controlled Fusion.

1. Overview of computer organization, hardware, software, scientific programming in FORTRAN and/or C, C++.

2. Numerical Techniques

Sorting, interpolation, extrapolation, regression, numerical integration, quadrature, random number generation, linear algebra and matrix manipulations, inversion, diagonalization, eigenvectors and eigenvalues, integration of initial-value problems, Euler, Runge-Kutta, and Verlet schemes, root searching, optimization, fast Fourier transforms.

3. Simulation Techniques

Monte Carlo methods, molecular dynamics, simulation methods for the Ising model and atomic fluids, simulation methods for quantum-mechanical problems, time-dependent Schrödinger equation, discussion of selected problems in percolation, cellular automata, nonlinear dynamics, traffic problems, diffusion-limited aggregation, celestial mechanics, etc.

4. Parallel Computation

Introduction to parallel computation.

References:

V. Rajaraman, Computer Programming in Fortran 77.

W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing. (Similar volumes in C, C++.)

H.M. Antia, Numerical Methods for Scientists and Engineers.

D.W. Heermann, Computer Simulation Methods in Theoretical Physics.

H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods.

- J.M. Thijssen, Computational Physics.

1. Introduction

Survey of network theorems and network analysis, AC and DC bridges, transistors at low and high frequencies, FET.

2. Electronic Devices

Diodes, light-emitting diodes, photo-diodes, negative-resistance devices, p-n-p-n characteristics, transistors (FET, MoSFET, bipolar).

Basic differential amplifier circuit, operational amplifier characteristics and applications, simple analog computer, analog integrated circuits.

3. Digital Electronics

Gates, combinational and sequential digital systems, flip-flops, counters, multi-channel analyzer.

4. Electronic Instruments

Power supplies, oscillators, digital oscilloscopes, counters, phase-sensitive detectors, introduction to micro-processors.

References:

P. Horowitz and W. Hill, The Art of Electronics.

J. Millman and A. Grabel, Microelectronics.

J.J. Cathey, Schaum's Outline of Electronic Devices and Circuits.

M. Forrest, Electronic Sensor Circuits and Projects.

W. Kleitz, Digital Electronics: A Practical Approach.

J.H. Moore, C.C. Davis and M.A. Coplan, Building Scientific Apparatus.

1. To trace I-V characteristic curves of diodes and transistors on a CRO, and learn their uses in electronic circuits.

2. Negative feedback and amplifier characteristics.

3. Uses of differential amplifier and opamps in linear circuits.

4.Design of simple logic gates using transistors.

5. To study transfer characteristics of a regenerative comparator, to design a time marker, sample, hold and multiplier circuits, to design a sweep generator using a Schmitt trigger.

6. AD/DA converter/GPIB interfacing.

7. Circuit simulation using SPICE.

8. Microwave generators.

9. Experiments with timers/pulse generators etc.

10. Digital electronics.

11. Microprocessor-based experiment.

12. Project (design of audio amplifier/digital clock/regulated power supply).

Note: Each student is required to perform at least 8 of the above experiments.

**Condensed Matter PhysicsPS 511**

1. Metals

Drude theory, DC conductivity, Hall effect and magneto-resistance, AC conductivity, thermal conductivity, thermo-electric effects, Fermi-Dirac distribution, thermal properties of an electron gas, Wiedemann-Franz law, critique of free-electron model.

2. Crystal Lattices

Bravais lattice, symmetry operations and classification of Bravais lattices, common crystal structures, reciprocal lattice, Brillouin zone, X-ray diffraction, Bragg's law, Von Laue's formulation, diffraction from non-crystalline systems.

3. Classification of Solids

Band classifications, covalent, molecular and ionic crystals, nature of bonding, cohesive energies, hydrogen bonding.

4. Electron States in Crystals

Periodic potential and Bloch's theorem, weak potential approximation, energy gaps, Fermi surface and Brillouin zones, Harrison construction, level density.

5. Electron Dynamics

Wave packets of Bloch electrons, semi-classical equations of motion, motion in static electric and magnetic fields, theory of holes.

6. Lattice Dynamics

Failure of the static lattice model, harmonic approximation, vibrations of a one-dimensional lattice, one-dimensional lattice with basis, models of three-dimensional lattices, quantization of vibrations, Einstein and Debye theories of specific heat, phonon density of states, neutron scattering.

7. Semiconductors

General properties and band structure, carrier statistics, impurities, intrinsic and extrinsic semiconductors, p-n junctions, equilibrium fields and densities in junctions, drift and diffusion currents.

8. Magnetism

Diamagnetism, paramagnetism of insulators and metals, ferromagnetism, Curie-Weiss law, introduction to other types of magnetic order.

9. Superconductors

Phenomenology, review of basic properties, thermodynamics of superconductors, London's equation and Meissner effect, Type-I and Type-II superconductors.

References:

C. Kittel, Introduction to Solid State Physics.

N.W. Ashcroft and N.D. Mermin, Solid State Physics.

J.M. Ziman, Principles of the Theory of Solids.

A.J. Dekker, Solid State Physics.

G. Burns, Solid State Physics.

M.P. Marder, Condensed Matter Physics.

1. Nuclear Physics

Discovery of the nucleus, Rutherford formula, form factors, nuclear size, characteristics of nuclei, angular momentum, magnetic moment, parity, quadrupole moment.

Mass defect, binding-energy statistics, Weiszacker mass formula, nuclear stability, Alpha-decay, tunnelling theory, fission, liquid drop model.

Nuclear forces, nucleon-nucleon scattering, deuteron problem, properties of nuclear potentials, Yukawa's hypothesis.

Magic numbers, shell model, calculation of nuclear parameters, basic ideas of nuclear reactions.

2. Particle Physics

Relativistic quantum theory, Dirac's equation and its relativistic covariance, intrinsic spin and magnetic moment, negative energy solution and the concept of antiparticle.

Accelerators and detectors,discovery of mesons and strange particles, isospin and internal symmetries, neutrino oscillations, quarks, parity violation, K-mesons, CP violation.

3. Weak Interactions

Fermi's theory of beta-decay, basic ideas of gauge symmetry, spontaneous symmetry breaking, elements of electro-weak theory, discovery of W-bosons.

4. Strong Interactions

Deep inelastic scattering, scaling concepts, quark model interpretation, colour quantum number, asymptotic freedom, quark confinement, standard model.

References:

G.D. Coughlan and J.E. Dodd, The Ideas of Particle Physics.

D. Griffiths, Introduction to Elementary Particles.

D.H. Perkins, Introduction to High Energy Physics.

I. Kaplan, Nuclear Physics.

R.R. Roy and B.P. Nigam, Nuclear Physics.

M.A. Preston and R.K. Bhaduri, Structure of the Nucleus.

M.G. Bowler, Nuclear Physics.

**Statistical Mechanics IIPS 513**

1. Phase Transitions and Critical Phenomena

Thermodynamics of phase transitions, metastable states, Van der Waals' equation of state, coexistence of phases, Landau theory, critical phenomena at second-order phase transitions, spatial and temporal fluctuations, scaling hypothesis, critical exponents, universality classes.

2. Ising Model

Ising model, mean-field theory, exact solution in one dimension, renormalization in one dimension.

3. Nonequilibrium Systems

Systems out of equilibrium, kinetic theory of a gas, approach to equilibrium and the H-theorem, Boltzmann equation and its application to transport problems, master equation and irreversibility, simple examples, ergodic theorem.

Brownian motion, Langevin equation, fluctuation-dissipation theorem, Einstein relation, Fokker-Planck equation.

4. Correlation Functions

Time correlation functions, linear response theory, Kubo formula, Onsager relations.

5. Coarse-grained Models

Hydrodynamics, Navier-Stokes equation for fluids, simple solutions for fluid flow, conservation laws and diffusion.

References:

K. Huang, Statistical Mechanics.

R.K. Pathria, Statistical Mechanics.

E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics.

D.A. McQuarrie, Statistical Mechanics.

L.P. Kadanoff, Statistical Physics: Statistics, Dynamics and Renormalization.

P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics.

1. Many-electron Atoms

Review of He atom, ground state and first excited state, quantum virial theorem, Thomas-Fermi method, determinantal wave function, Hartree and Hartree-Fock method, periodic table and atomic properties: ionization potential, electron affinity, Hund's rule.

2. Molecular Quantum Mechanics

Hydrogen molecular ion, hydrogen molecule, Heitler-London method, molecular orbital, Born-Oppenheimer approximation, bonding, directed valence.

3. Atomic and Molecular Spectroscopy

Fine and hyperfine structure of atoms, electronic, vibrational and rotational spectra for diatomic molecules, role of symmetry, selection rules, term schemes, applications to electronic and vibrational problems.

4. Second Quantization

Basis sets for identical-particle systems, number space representation, creation and annihilation operators, representation of dynamical operators and the Hamiltonian, simple applications.

5. Interaction of Atoms with Radiation

Atoms in an electromagnetic field, absorption and induced emission, spontaneous emission and line-width, Einstein A and B coefficients, density matrix formalism, two-level atoms in a radiation field.

References:

I.N. Levine, Quantum Chemistry.

R. McWeeny, Coulson's Valence.

L.D. Landau and E.M. Lifshitz, Quantum Mechanics.

M. Karplus and R.N. Porter, Atoms and Molecules: An Introduction for Students of Physical Chemistry.

P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics.

M. Tinkham, Group Theory and Quantum Mechanics.

L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems.

W.A. Harrison, Applied Quantum Mechanics.

1. Electron-spin resonance.

2. Faraday rotation/Kerr effect.

3. Interfacial tension and Phase separation kinetics.

4. Reaction kinetics by spectrophotometer and conductivity.

5. Study ofcolor centres by spectrophotometer.

6. Alpha, Beta and Gamma ray spectrometer.

7. Mössbauer spectrometer.

8. Sizing nano-structures (UV-VIS spectroscopy).

9. Magneto-resistance and its field dependence.

10. X-ray diffraction.

11. Compton scattering.

12. Adiabatic compressibility.

13. Solid-liquid phasediagram for a mixture.

Note: Each student is required to perform at least 8 of the above experiments.

**Modern Experiments: A SurveyPS 521**

Note: This course will familiarize students with some landmark experiments in physics through the original papers which reported these experiments. A representative list is as follows:

1. Mössbauer effect.

2. Pound-Rebka experiment to measure gravitational red shift.

3. Parity violation experiment of Wu et al.

4. Superfluidity of He3.

5. Cosmic microwave background radiation.

6. Helicity of the neutrino.

7. Quantum Hall effect - integral and fractional.

8. Laser cooling of atoms.

9. Ion traps.

10. Bose-Einstein condensation.

11. Josephsontunneling.

12. Atomic clocks.

13. Interferometry for gravitational waves.

14. Quantum entanglement experiments: Teleportation experiment, Aspect's experiment on Bell's inequality.

15. Inelastic neutron scattering.

16. CP violation.

17. J/Psi resonance

18. Verification of predictions ofgeneral theory of relativity by binary-pulsar and other experiments.

19 Precision measurements ofmagnetic moment of electron.

20. Libchaber experiment on period-doubling route to chaos.

21. Anfinson's experiment on protein folding.

22. Scanning tunnelling microscope.

**Astrophysics, Gravitation and CosmologyPS 523**

1. Physics of the Universe

Astronomical observations and instruments, stellar spectra and structure, stellar evolution, nucleosynthesis and formation of elements, evolution and origin of galaxies, quasars, pulsars, expansion of the universe, big-bang model, CMBR, anisotropy.

2. General Relativity

Review of special theory of relativity, four-vector formulation of Lorentz transformation, covariant formulation of physical laws, introduction to general relativity, principle of equivalence, tensor analysis and Riemannian geometry, curvature and stress-energy tensors, gravitational field equations, geodesics and particle trajectories, Schwarschild solution, Kerr solution, gravitational waves, relativistic stellar structure, TOV equation, basic cosmology.

References:

- K.D. Abhyankar, Astrophysics: Stars and Galaxies.
- J.V. Narlikar, An Introduction to Cosmology.
- C.W. Misner, K. Thorne, J.A. Wheeler, Gravitation.
- R. Adler, M. Bazin and M. Schiffer, Introduction to General Relativity.
- T. Padmanabhan, Cosmology and Astrophysics through Problems.

1. String waves, water waves, etc. as examples of classical fields, Lagrangian and Hamiltonian formulation of a vibrating string fixed at both ends in analogy with Newtonian particles.

2. Relativistic kinematics, relativistic waves, Klein-Gordon (KG) equation as a relativistic wave equation, treatment of the KG equation as a classical wave equation: its Lagrangian and Hamiltonian, Noether's theorem and derivation of energy-momentum and angular momentum tensors as consequence of Poincaré symmetry, internal symmetry and the associated conserved current.

3. Canonical quantization of the KG field,solution of KG theory in Schrödinger and Heisenberg pictures, expansion in terms of creation and annihilation operators, definition of the vacuum and N-particle eigenstates of the Hamiltonian, vacuum expectation values, propagators, spin and statistics of the KG quantum.

4. Review of Dirac equation and its quantization, useof anti-commutators, creation and destruction operators of particles and antiparticles, Dirac propagator, energy, momentum and angular momentum, spin and statistics of Dirac quanta.

5. Review of free Maxwell's equations, Lagrangian, gauge transformation and gauge fixing, Hamiltonian, quantization in terms of transverse delta functions, expansion in terms of creation operators, spin, statistics and propagator of the photon.

6. Introduction to interacting quantum fields.

References:

- C. Itzykson and J.-B. Zuber, Quantum Field Theory.
- J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields.
- L. Ryder, Quantum Field Theory.
- V.B. Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Quantum Electrodynamics.
- M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory.

1. Introduction

Evolution of biosphere, aerobic and anaerobic concepts, models of evolution of living organisms.

2. Physics of Polymers

Nomenclature, definitions of molecular weights, polydispersity, degree of polymerization, possible geometrical shapes, chirality in biomolecules, structure of water and ice, hydrogen bond and hydrophobocity.

3. Static Properties

Random flight model, freely-rotating chain model, scaling relations, concept of various radii (i.e., radius of gyration, hydrodynamic radius, end-to-end length), end-to-end length distributions, concept of segments and Kuhn segment length, excluded volume interactions and chain swelling, Gaussian coil, concept of theta and good solvents with examples, importance of second virial coefficient.

4. Polyelectrolytes

Concepts and examples, Debye-Huckel theory, screening length in electrostatic interactions.

5. Transport Properties

(a) Diffusion: Irreversible thermodynamics, Gibbs-Duhem equation, phenomenological forces and fluxes, osmotic pressure and second virial coefficient, generalized diffusion equation, Stokes-Einstein relation, diffusion in three-component systems, balance of thermodynamic and hydrodynamic forces, concentration dependence, Smoluchowski equation and reduction to Fokker-Planck equation, concept of impermeable and free-draining chains.

(b) Viscosity and Sedimentation: Einstein relation,intrinsic viscosity of polymer chains, Huggins equation of viscosity, scaling relations, Kirkwood-Riseman theory, irreversible thermodynamics and sedimentation, sedimentation equation, concentration dependence.

6. Physics of Proteins

Nomenclature and structure of amino acids, conformations of polypeptide chains, primary, secondary and higher-order structures, Ramachandran map, peptide bond and its consequences, pH-pK balance, protein polymerization models, helix-coil transitions in thermodynamic and partition function approach, coil-globule transitions, protein folding, protein denaturation models, binding isotherms, binding equilibrium, Hill equation and Scatchard plot.

7. Physics of Enzymes

Chemical kinetics and catalysis, kinetics of simple enzymatic reactions, enzyme-substrate interactions, cooperative properties.

8. Physics of Nucleic Acids

Structure of nucleic acids, special features and properties, DNA and RNA, Watson-Crick picture and duplex stabilization model, thermodynamics of melting and kinetics of denaturation of duplex, loops and cyclization of DNA, ligand interactions, genetic code and protein biosynthesis, DNA replication.

9. Experimental Techniques

Measurement concepts and error analysis, light and neutron scattering, X-ray diffraction, UV spectroscopy, CD and ORD, electrophoresis, viscometry and rheology, DSC and dielectric relaxation studies.

10. Recent Topics in Bio-Nanophysics

References:

M.V. Volkenstein, General Biophysics.

C.R. Cantor and P.R. Schimmel, Biophysical Chemistry Part III: The Behavior of Biological Macromolecules.

C. Tanford, Physical Chemistry of Macromolecules.

S.F. Sun, Physical Chemistry of Macromolecules: Basic Principles and Issues.

1. Introduction

Masers versus lasers, components of a laser system, amplification by population inversion, oscillation condition, types of lasers: solid-state (ruby, Nd:YAG, semiconductor), gas (He-Ne, CO2 excimer), liquid (organic dye) lasers.

2. Atom-Field Interactions

Lorenz theory, Einstein's rate equations, applications to laser transitions with pumping, two, three and four-level schemes, threshold pumping and inversion.

3. Optical Resonators

Closed versus open cavities, modes of a symmetric confocal optical resonator, stability, quality factor.

4. Semi-classical Laser Theory

Density matrix for a two-level atom, Lamb equation for the classical field, threshold condition, disorder-order phase transition analogy.

5. Coherence

Concepts of coherence and correlation functions, coherent states of the electromagnetic field, minimum uncertainty states, unit degree of coherence, Poisson photon statistics.

6. Pulsed Operation of Lasers

Q-switching, electro-optic and acousto-optic modulation, saturable absorbers, mode- locking.

7. Applications of Lasers

Introduction to atom optics, Doppler cooling of atoms, introduction to nonlinear optics: self-(de) focusing, second-harmonic generation (phase-matching conditions).

References:

K. Thyagarajan and A.K. Ghatak, Lasers: Theory and Applications.

A.K. Ghatak and K. Thyagarajan, Optical Electronics.

W. Demtroeder, Laser Spectroscopy.

B.B. Laud, Lasers and Nonlinear Optics.

M. Sargent III, M.O. Scully and W.E. Lamb, Jr., Laser Physics.

M.O. Scully and M.S. Zubairy, Quantum Optics.

P. Meystre and M. Sargent III, Elements of Quantum Optics.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics.

**Advanced Condensed Matter PhysicsPS 527**

1. Dielectric Properties of Solids

Dielectric constant of metal and insulator using phenomenological theory (Maxwell's equations), polarization and ferroelectrics, inter-band transitions, Kramers-Kronig relations, polarons, excitons, optical properties of metals and insulators.

2. Transport Properties of Solids

Boltzmann transport equation, resistivity of metals and semiconductors, thermoelectric phenomena, Onsager coefficients.

3. Many-electron Systems

Sommerfeld expansion, Hartree-Fock approximation, exchange interactions, concept of quasi-particles, introduction to Fermi liquid theory, screening, plasmons.

4. Introduction to Strongly Correlated Systems

Narrow band solids, Wannier orbitals and tight-binding method, Mott insulator, electronic and magnetic properties of oxides, introduction to Hubbard model.

5. Magnetism

Magnetic interactions, Heitler-London method, exchange and superexchange, magnetic moments and crystal-field effects, ferromagnetism, spin-wave excitations and thermodynamics, antiferromagnetism.

6. Superconductivity

Basic phenomena, London equations, Cooper pairs, coherence, Ginzburg-Landau theory, BCS theory, Josephson effect, SQUID, excitations and energy gap, magnetic properties of type-I and type-II superconductors, flux lattice, introduction to high-temperature superconductors.

References:

N.W. Ashcroft and N.D. Mermin, Solid State Physics.

D. Pines, Elementary Excitations in Solids.

S. Raimes, The Wave Mechanics of Electrons in Metals.

P. Fazekas, Lecture Notes on Electron Correlation and Magnetism.

M. Tinkham, Introduction to Superconductivity.

M. Marder, Condensed Matter Physics.

1. Introduction to Dynamical Systems

Physics of nonlinear systems, dynamical equations and constants of motion, phase space, fixed points, stability analysis, bifurcations and their classification, Poincaré section and iterative maps.

2. Dissipative Systems

One-dimensional noninvertible maps, simple and strange attractors, iterative maps, period-doubling and universality, intermittency, invariant measure, Lyapunov exponents, higher-dimensional systems, Hénon map, Lorenz equations, fractal geometry, generalized dimensions, examples of fractals.

3. Hamiltonian Systems

Integrability, Liouville's theorem, action-angle variables, introduction to perturbation techniques, KAM theorem, area-preserving maps, concepts of chaos and stochasticity.

4. Advanced Topics

Selections from quantum chaos, cellular automata and coupled map lattices, pattern formation, solitons and completely integrable systems, turbulence.

References:

E. Ott, Chaos in Dynamical Systems.

E.A. Jackson, Perspectives of Nonlinear Dynamics (Volumes 1 and 2).

A.J. Lichtenberg and M.A. Lieberman, Regular and Stochastic Motion.

A.M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization.

M. Tabor, Chaos and Integrability in Nonlinear Dynamics.

M. Lakshmanan and S. Rajasekar, Nonlinear Dynamics: Integrability, Chaos and Patterns.

H.J. Stockmann, Quantum Chaos: An Introduction.