Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This is a course which aims to prepare students with advanced concepts, techniques and knowledge of solid state physics that allows them to start working on basic research problems in the broad area of condensed matter theory, materials theory or solid state experiments.

Syllabus:

• Introduction to Fermi liquid theory, quasiparticle, spectral function properties and metal to insulators transitions. Idea of non Fermi liquid metals.
• Local moment formation and suppression in metals.
• Collective excitations: screening and plasma oscillations, spin waves and magnons.
• Electrical and optical properties of Fermi liquid metals and Mott insulators
• Charge impurity in a metal and Friedel oscillation
• Magnetic impurity in a metal: quenching of local moments (Kondo effect)
• Electron phonon interaction: electrical conduction, sound propagation and ultrasonic attenuation.
• Quantum Hall Effect: Landau levels, role of disorder, Laughlin states and composite fermions (time permitting), introduction to topological protection and Chern insulators.
• Band theory and simple topological insulators. 10. Quantum phase transition: Quantum rotor model, mean field solution, scaling and transport properties.

Reference Book

1. Concepts in Solids by P. W. Anderson
2. Advanced Solid State Physics by P. Philips
3. Elementary Excitations in Solids by D. Pines
4. Introduction to Many-Body Physics by P. Coleman
5. Lecture Notes on Electron Correlation and Magnetism by P. Fazekas
6. Condensed Matter Physics by M. P. Marder
7. Strong Fermion Interactions in Fractional Quantum Hall States: Correlation Functions by S. Mulay, J. J. Quinn, M. Shattuck
8. Composite Fermions by Jainendra K. Jain
9. Quantum phase transition by Subir Sachdev

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course provides training in computation tools required in research across a wide variety of fields including condensed matter, high energy phenomenology and lattice field theories.

Syllabus:

• Introduction to theory of computation and Random numbers.
• Monte Carlo: Importance sampling, Markov chain, Metropolis algorithm, Ising Model and other applications.
• Molecular Dynamics: Integration methods (e.g Verlet and Leap frog algorithms), extended ensembles, molecular system.
• Variational methods for Schrodinger Equation, Hartree and Hartee-Fock methods.
• Quantum Monte Carlo methods.
• Special Topics Like: QMD, Ideal fluids, matrix inversions, Numerical solution of Poisson’s equation: Finite difference method. Particle-Mesh Methods, radiative transfer etc.

Reference Book

1. Computational Physics by Joseph Marie Thijssen, Cambridge University Press
2. An Introduction to Computational Physics by Tao Pang, Cambridge University press
3. Computer Simulation of Liquid by M. P. Allen and D. J. Tildesley, Clarendon press
4. A Guide to Monte Carlo Simulations in Statistical Physics by L. Landau and K. Binder
5. Quantum Monte Carlo Methods by M. Suzuki (Editor) Springer-Verlag
6. New Methods in Computational Quantum Mechanics by I. Prigogine and Stuart A. Rice
7. Understanding Molecular Simulation by D. Frankel and B. Smit, Second edition, academic press.
8. Computational Methods in Field Theory by H. Gausterer and C.B. Lang (Lecture notes in physics 409)
9. Density Functional Theory of Atoms and Molecules by R. G. Parr and W. Yang
10. F. Jensen, introduction to Computational Chemistry by F. Jensen
11. Essentials of Computational Chemistry by C. J. Crammer
12. Dynamical mean field theory by Jean-Marc Robin
13. Quantum Monte Carlo Methods by James Gubernatis, Naoki Kawashima, Philipp Werner
14. Computer Simulations using Particles - R. W. Hockney and J. W. Eastwood

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This first course on quantum field theory prepares the student for tackling future advanced courses in the area of high energy physics.

Syllabus:

• Relativistic quantum mechanics - Klein-gordon equation, Dirac equation, free- particle solutions
• Lagrangian formulation of Klein-Gordon, Dirac and Maxwell equations, Symmetries (Noether’s theorem), Gauge field, actions
• Canonical quantization of scalar and Dirac fields
• Interacting fields - Heisenberg picture, perturbation theory, Wicks theorem, Feynman diagram
• Cross-section and S-matrix
• Quantization of gauge field, gauge fixing
• QED and QED processes
• Radiative corrections - self-energy, vacuum polarization, vertex correction
• LSZ and optical theorem 10. Introduction to re-normalization

Reference Book

1. An Introduction to Quantum Field Theory by M. Peskin and D. V. Schroeder
2. Quantum Field theory: From Operators to Path Integrals, 2nd edition by Kerson Huang
3. Quantum Field Theory by Mark Srednicki
4. Quantum Field Theory by Claude Itzykson and Jean Bernard Zuber
5. Notes from Sidney Coleman's Physics 253a, arXiv: 1110.5013

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the basics of particle physics and allows the student to start beginning research work in high energy phenomenology

Syllabus:

• Elementary particles, discrete symmetries and conservation laws.
• Symmetries and Quarks.
• Klein-Gordon equation, concept of antiparticle.
• Lorentz symmetry and scalar / vector / spinor fields.
• Dirac equation
• Scattering processes of spin-1/2 particles, Feynmans rules as thumb rule QFT course, propagators.
• Current-current interactions, weak interaction, Fermi theory.
• gauge symmetries, spontaneous symmetry breaking, Higgs mechanism 9. Electroweak interaction, Glashow-Salam-Weinberg model. 10. Introduction to QCD, structure of hadrons form factors, structure functions, parton model, Deep inelastic scattering.

Reference Book

1. Gauge Theories in Particle Physics, Vol I & II by Aitchison and Hey
2. Foundations of Quantum Chromodynamics by T. Muta
3. Modern Particle Physics by Mark Thomson
4. Introduction to Elementary Particle by David Griffiths
5. Quarks and Leptons by F. Halzen and A.D. Martin
6. Introduction to High Energy Physics: D.H. Perkins
7. Introduction to Elementary Particle Physics: A. Bettini
8. Particle Physics by B. R. Martin and G. Shaw

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students advanced concepts and methods in statistical mechanics crucial for the student to take up basic research work.

Syllabus:

• Introduction to critical phenomena and first order phase transition. Survey of experimental results and scaling hypothesis, introduction to critical exponents and universality.
• Review of thermodynamic potentials, introduction to order parameter and response functions.
• Introduction to interacting systems: study of one dimensional Ising model via transfer matrix, lack of phase transition in one dimension, study of Ising model in two dimensions, XY and Heisenberg model.
• Mean field theory: calculation of order parameter, response functions and correlation functions using Curie-Weiss mean field theory and Landau-Ginzberg theory, calculation of critical exponents for mean field systems, range of validity of mean field theory.
• Introduction to re-normalization group (RG): Kadanoff block spins and real space RG methods, Perturbative RG in momentum space: Wilson-Fisher RG and epsilon expansion, broken continuous symmetry: Mermin Wagner theorem, Goldstone modes and Kosterlitz Thouless phase transition, introduction to non-linear sigma models, quantum critical phenomena and quantum phase transitions, introduction to 1D Transverse Field Ising Model and introduction to Bose- Hubbard model.

Reference Book

1. Introduction to phase Transitions and Critical phenomena by H. Eugene Stanley
2. Modern approach to Critical phenomena by Igor Herbut
3. Statistical physics: Statics, Dynamics and Renormalization by Leo p. Kadanoff
4. The Theory of Critical phenomena by J. J. Binney, a. J. Fisher, M. E. J. newman
5. Modern Theory of Critical phenomena by Shang-keng Ma
6. Statistical Mechanics of phase Transitions by J. Yeomans
7. Field Theory, the Renormalisation group and Critical phenomena by Daniel J. Amit

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students advanced concepts and methods in modern topics in laser optics and nonlinear optics necessary for the student to take up basic research work in optics.

Syllabus:

• Introduction to general lasers and their types, emission, absorption processes and rate equations, population inversion, gain, optical cavities, three and four level lasers, CW and pulsed lasers, Qswitching and mode-locking, physics of gas discharge, atomic, ionic, molecular, liquid, and excimer lasers, optical pumping, Holography
• Overview of non- linear Optics, nonlinear polarization, nonlinear optical susceptibility, Symmetry considerations
• Wave propagation in nonlinear media
• Electro optical and magneto optical effects
• Higher harmonic generations, phase matching and quasi phase matching, Sum and difference frequency generation, Optical parametric amplification and oscillation
• Kerr effect, Cross-Phase Modulation, Self phase modulation, Multi-photon processes , Self focusing, Four-Wave Mixing
• Laser Spectroscopy, wave front conjugation Stimulated Raman Scattering, Stimulated Brillouin Scattering, Optical solitons and Optical pulse compression

Reference Book

1. Lasers by P. W. Milonni and J. H. Eberly
2. Lasers by A. E. Siegman
3. Principles of Lasers by Orazio Svelto
4. The Principles of Nonlinear Optics by Y. R. Shen
5. Nonlinear Optics by Robert W. Boyd
6. Nonlinear Optics: Basic Concepts by D. L. Mills
7. Optical waves in crystals by Amnon Yariv and Pochi Yeh

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students, advanced concepts and methods in general relativity crucial for the student for building their background for research work in general relativity and cosmology.

Syllabus:

• Review of Newtonian Mechanics. Special theory of relativity. prelude to general relativity, historical developments
• 4-Vectors and 4-tensors, examples from physics
• Principle of Equivalence, Equations of motion, gravitational force
• Tensor analysis in Riemannian space, Effects of gravitation, Riemann-Christoffel curvature tensor, Ricci Tensor, Curvature Scalar
• Einstein Field Equations, Experimental tests of GTR
• Schwartzchild Solution, gravitational lensing
• Gravitational waves: generation and detection
• Energy, momentum and angular momentum in gravitation
• Cosmological principle, Robertson-Walker metric, Redshifts
• Big-Bang Hypothesis, CMB
• Issues in Quantum gravity

Reference Book

1. A first course in General Relativity by Bernard Schutz
2. Gravity by James B. Hartle
3. The Classical Theory of Fields by L. D. Landau and E. M. Lifshitz
4. Gravitation and Cosmology by Steven Weinberg
5. Introducing Einstein's Relativity by Ray D'Inverno
6. General Relativity by P. Dirac

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students advanced concepts and methods in soft matter physics, with the aim to build their background for future research work in this area.

Syllabus:

• Introduction: Basic phenomenology of soft condensed matter systems, intermolecular forces, viscoelasticity, ordering in softmatter, glass transition, phase separation
• Diffusion processes: Fick’s laws, Diffusion Equation, Random walks, Brownian motion, Langevin and Fokker-Plank equations
• Colloids: Stability of colloidal systems, Poisson-Boltzmann theory, DLVO theory, Depletion interactions, Electro-kinetic effects
• Polymers: model systems and chain statistics, polymers in solvents and melts, viscoelasticity, gelation
• Liquid crystals: Introduction, liquid crystal phases and transitions, Distorted nematic ordering, response to electric and magnetic fields
• Amphiphiles: Introduction, microphase separation in block copolymers and in solutions of amphiphiles, aggregation and self-assembly of amphiphiles

Reference Book

1. Principles of Condensed Matter Physics by P. M. Chaikin and T. C. Lubensky
2. Soft Condensed Matter by R. A. L. Jones
3. Structured Fluids: Polymers, Colloids, Surfactants by T. Witten
4. Introduction to Soft Matter: Polymers, Colloids, Amphiphiles and Liquid Crystals by I. W. Hamley
5. Soft Matter Physics by M. Klemanand and O. D. Lavrentovich
6. Colloidal Dispersions by W. B. Russel, D. A. Saville and W. R. Showalter
7. Dynamics of Colloids by J. K. G. Dont
8. Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems by J. Israelachvili
9. Introduction to Liquid Crystals  by P. J. Collings and M. Hird
10. Polymer solutions -- an introduction to physical properties by I. Teraoka

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students advanced concepts and methods in applied nuclear physics, with the aim to build their background for future research work in this area.

Syllabus:

• Basis of nuclear structure andreactions
• Radioactivity and radioactivedecays: Detecting nuclear radiations, Alpha decay, beta decay, gamma decay
• Passage of charged particle throughmatter.
• Detectors andaccelerators.
• Applications: Effects of radiation on biological systems and Nuclear medicine, Industrial Applications
• Power from Fission and Fusion: Characteristics of Fission, Nuclear Reactors, Thermonuclearfusion

Reference Book

1. Nuclear Physics: Principles andApplications,John Lilley, Wiley Publications
2. TheAtomicNucleus,Robley D. Evans, Tata McGraw-Hill Publishing.
3. Fundamentals of Nuclear Reactor Physics, Elmer Lewis, Elsevier Publishing.
4. An Introduction to the Passage of Energetic Particlesthrough Matter, N.J.Carron, CRC Press
5. Accelerator Physics, S. Y. Lee, World Scientific

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students advanced concepts and methods in many particle physics, with the aim to build their background for future research work in this area.

Syllabus:

• Review of second quantisation, one and two body operators, mean field solutions of interacting systems.
• CanonicalTransformation: Jordan-Wigner, Bogoliubov-Valetin, SchriefferWolf,etc.
• Green's function formalism at zero & finite temperatures, observables and their relationship to one and two body Greens functions.
• Thermodynamic potential, spectral functions, analytic properties of Green’s function.
• Linear Response, correlation function, sum rules.
• Green’s functions equation of motion.
• Diagrammaticperturbationtheory for Greenfunction and the thermodynamic potential. Interacting fermions: Hartree-Fock, Random phase and ladder approximation, Goldstone theorem, Luttinger Ward identities. Interacting bosons: condensate depletion.
• Functional methods: Imaginary time and coherent state path integrals, many particle partition function and perturbation theory in path integral approach. Stationary phase approximation. Hubbard-Stratonovich transformationand auxiliary field representation of time evolution operator and the partition function. Saddle point approximation and small fluctuation corrections.

Reference Book

1. Statistical Physics part 2 by E.M.Lifshitz& L.P. Pitaevskii
2. Quantum Theory of Many body particle systems by FetterWalecka
3. Introduction to Many-Body Physics by Piers Coleman
4. Many particle physics by Ben Simon
5. Green’s Function for SolidState Physics by S. Doniach & E.H. Sondheimer
6. Quantum Mechanics R. Shankar
7. Quantum many particle systems J. W. Negele and H. Orland
8. Techniques and Application of Path-integration by S.Schulman

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students advanced concepts and methods in mesoscopic physics, with the aim to build their background for future research work in this area.

Syllabus:

• Effects of magnetic fields: TheAharonov Bohm effect; 2D electron gas; Landau levels; Transverse modes in 2D quantum wire; Shubnikovde Haas oscillations; Magnetic edge states; integer Quantum Hall effect, Fractional Quantum Hall effect
• Electron transport: Boltzmann semiclassical transport; Onsager reciprocity relations; Conventional Hall effect; Drude conductivity; Einstein relation; Electronic states in quantum confined systems; Conductance from transmission; Ballistic transport; Quantum of conductance; Landauer formula; Quantum point contact; T-matrices; S-matrix and green functions; Current operator; Landauer Buttiker formalism; Linear response and Kubo formula; nonequilib- rium green’s function approach to transport; Scattering: Breit Wigner resonance and Fano resonance; Delay time for resonances; Friedel sum rule; Levin- son.s theorem; Singleelectron tunneling: Coulomb blockade and Kondoeffect
• Quantum information: Josephson Junctions and Cubits; Metastable states and escapedynamics
• Disordered conductors: Weak localization; Mesoscopic fluctuations; Random Matrices; Anderson localization; Quantum Chaos; Dephasing; Decoherence

Reference Book

1. Electronic Transport in Mesoscopic Systems by S. Datta, Cambridge University press.
2. Introduction to Mesoscopic Physics by Y. Imry
3. Mesoscopic Electronics in Solid State Nanostructures by T. Heinzel
4. Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations by P. Mello and N. Kumar

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in quantum optics, with the aim to build their background for future research work in this area.

Syllabus:

• Electromagnetic field quantization: Quantum fluctuation and Quadrature operators of a single mode field, Thermal fields, Vacuum fluctuation and zero point energy, Quantum phase
• Coherent and squeezed states of radiation field: Properties and phase space picture of coherent state, Generation of a coherent state, Squeezed state physics, generation and Detection of squeezed light, Schrodinger cat states, Multi- mode squeezing, Broadband squeezed light, Squeezing via non-linear process
• Atom-field interaction: Rabi model (Semi-classical model for atom-field interaction), Jaynes-Cummings model (fully quantum mechanical model for atom- field interaction), Dressed states, Density operator approach, Hanle effect, Coherent trapping, electromagnetically induced transparency, Four wave mixing
• Quantum coherence function: photon detection and quantum coherence functions, First order coherence and Youngs type double source experiment, Second order coherence, physics of Hanbury-Brown-Twiss effect, Experiments with single photon, Quantum mechanics of beam splitter, interferometry with single photon
• Optical test of quantum mechanics: photon sources: spontaneous parametric down-conversion, Hong-Ou-Mandel interferometer, Superluminal tunneling of photons, EpR paradox and optical test of Bell.s theorem
• atom Optics: Mechanical effects of light, Laser cooling, atom interferometry, atoms in cavity, Experimental realization of Jaynes-Cummings model
• Heisenberg-limitedinterferometryandquantuminformation:Entanglementandinterferometricmeasurements,Quantum teleportation, Quantum cryptography, an optical realization of some quantum gates.

Reference Book

1. Introductory Quantum Optics by C. C. Gerry and P. L. Knight, Cambridge University  press
2. Quantum Optics by M. O. Scully and  M. S. Zubairy, Cambridge University press
3. Quantum Optics by M. Fox, Oxford Master series in atomic, Optical and Laser physics
4. Quantum Theory of Light by R. Loudon, Oxford science publication

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in astronomy and astrophysics, with the aim to build their background for future research work in this area.

Syllabus:

Part I: Introduction and Tools

• Tools - astronomical objects, scales, distance ladder, astrometry, magnitude scale
• Gravity - Kepler’s law, Virial theorem
• Radiation physics - radiative flux, transfer function, absorption, scattering and emission, Einstein coefficient, local thermodynamic equilibrium, source function and line formation, concept of opacities

Part II: Stars

• Stars and stellar structures - stellar spectra, HR diagram • Equilibrium in stars
• Star formation and Protostar
• Stellar evolution
• Supernovae
• Black holes and gravitational waves

Part III : Interstellar medium

Part IV: Galaxies

• The Milky way Galaxy - distribution of matter, differential rotation, formation of the spiral arms
• Elliptical and Spiral Galaxies
• Evidence for dark matter
• Active Galaxies - Active Galactic Nuclei, Seyfert Galaxies, Quasars, Blazers

Part V: Magnetic Fields

• Astrophysical phenomena where magnetic fields are critical
• Galactic magnetic fields - dust and synchrotron polarization, Faraday rotation, Zeeman measurements

Part VI: Gravitational Lensing

Part VII: Clusters and Superclusters (optional)

Part VIII: Cosmology (optional)

• Cosmological Observations and the Cosmological Principle
• Newtonian Cosmology and Cosmological Models
• Cosmic Microwave Background

Reference Book

1. Fundamental Astronomy by H. Karttunen, P. Kröger, H. Oja, M. Poutanen, K. J. Donner
2. Introduction to Modern Astrophysics by B. W. Carroll and D. A. Ostlie
3. An invitation to Astrophysics by T. Padmanabhan
4. Astrophysical Concepts by Martin Harwit
5. Introductory Astronomy and Astrophysics by Zelike and Gregory
6. Universe by Roger Freedman
7. Physical Universe by F. Shu
8. Astrophysics Processes by Hale Bradt
9. Radiative processes in Astrophysics by Rybicki and Lightman
10. An introduction to Astronomy and Astrophysics by Pankaj Jain
11. Quasars and Active Galactic Nuclei by Kembhavi and Narlikar

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in plasma physics and magnetohydrodynamics, with the aim to build their background for future research work in this area.

Syllabus:

• Introduction to plasmas, applications: in fusion, space and astrophysics, semi- conductor etching, micro- wave generation, characterisation of the plasma state, Debye shielding.
• Plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single charged particles.
• Two-fluid description, magneto-hydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping.
• Ideal magneto-hydrodynamic (MHD) equilibrium, MHD energy principle, ideal and resistive MHD stability, drift-kinetic equation, collisions, classical and neoclassical transport, drift waves and low frequency instabilities, high frequency micro instabilities, and quasi-linear theory.

Reference Book

1. Plasma physics by Peter Andrew Sturrock
2. Principles of Magnetohydrodynamics by J. P. Hans Goedbloed, Stefaan Poedts
3. Hydrodynamic and Hydromagnetic Stability by S. Chandrasekhar
4. The Physics of Plasmas by T. J. M. Boyd, J. J. Sanderson
5. Fundamentals of Plasma Physics by Paul M. Bellan,
6. Introduction to Plasma Physics by R. J. Goldston, P. H. Rutherford
7. An Introduction to Magnetohydrodynamics by P. A. Davidson
8. An Introduction to Plasma Astrophysics and Magnetohydrodynamics by M. Goossens

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in nanoelectronics, with the aim to build their background for future research work in this area.

Syllabus:

• Introduction and review of electronic technology
• From electronics to nano-electronics: particles, waves and Schrodinger equation, quantum description of atoms and molecules, quantum description of metals, semiconductors, junction devices, some newer building blocks for nano-electronic devices
• Fabrication and characterization methods for nano-electronics
• The field effect transistor FET: size limits and alternative forms
• Devices based on electron tunneling, resonant tunnel diodes, single electron transistors, molecular electronics, hybrid electronics
• Devices based on electron spin and ferromagnetism
• Qubits vs. binary bits in a quantum computer, applications of nano-electronic technology to energy issues
• Summary and brief comment on the future of nano-electronic techniques

Reference Book

1. Quantumnano-electronics:AnIntroductiontoElectronicNanotechnologyandQuantumComputingby Edward L.Wolf
2. Quantum Electronics by Amnon Yariv
3. Nanophysics and Nanotechnology:An Introduction to Modern Conceptsin Nanoscience by Edward L. Wolf
4. Fundamentals of Nanoelectronics by George Hanson
5. Introduction to Nanoelectronics: Science, Nanotechnology, Engineering and Applications by Vladimir Mitin, Viatcheslav, A. Kochelap, Michael, A. Stroscio

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in classical nonlinear dynamics, with the aim to build their background for future research work in this area.

Syllabus:

• General introduction and motivation: examples of linearity and nonlinearity in physics and the other sciences; modelling systems using iterated maps or differential equations, nonautonomous systems
• General features of dynamical systems : Systems of differential equations with examples; control parameters; fixed points and their stability; phase space; linear stability analysis; numerical methods for nonlinear systems; properties of limit cycles; nonlinear oscillators and their applications; the impossibility of chaos in the phase plane; bifurcations: their classification and physical examples; spatial systems, pattern formation and the Turing mechanism; strange attractors and chaotic behaviour.
• The logistic map: Linear and quadratic maps; graphical analysis of the logistic map; linear stability analysis and the existence of 2-cycles; numerical analysis of the logistic map; chaotic behaviour and the determination of the Lyapunov exponent; universality and the Feigenbaum numbers; other examples of iterated maps.
• Hamiltonian Sytems: Phase space; Constants of motion and integrable Hamiltonians; Nonintegrable systems, the KAM theorem and period-doubling; applications.
• Fractal geometry: dimension of an object, Mandelbrot set, Julia set, iterated function systems.
• Spatio-temporal dynamics: Spatio-temporal chaos.
• Quantum Chaos: Quantum analogies to Chaotic behaviour, Correaltions in wave functions, chaos and Semi-classical approaches to Quantum mechanics.

Reference Book

1. Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry and Engineering by S. H. Strogatz
2. Chaos and Nonlinear Dynamics by Robert C. Hilborn
3. Exploring Chaos: Theory and Experiment by Brian Davies
4. An Introduction to Dynamical Systems by K. T. Alligood, T. D. Sauer and J. A. Yorke, Chaos
5. Chaos in Dynamical Systems by Edward Ott
6. Chaos and Integrability in Nonlinear Dynamics: An Introduction by M. Tabor

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and applications of many particle quantum mechanics, with the aim to build their background for future research work in this area.

Syllabus:

• The phenomenon of Superconductivity: historical perspective, characteristics, occurrence
• London Equations, Thermodynamics
• Ginzburg Landau Theory, Abrikosov Vortices
• Josephson Effect
• Cooper instability, BCS wave function, gap equation, thermodynamics and magnetic response, Nambu-Gorkov formalism, idea of BCS-BEC crossover.
• Conventional and non-conventional superconductors
• Diamagnetism paramagnetism Ferromagnetism characteristics, Occurrence
• Orbital magnetism, de Haas van Alfen effect, Meissner Effect in superconductor
• Heisenberg Model: ground state, spin waves
• Hubbard Model and itinerant exchange

Reference Book

1. Theoryof Superconductivityby J. R. Schrieffer
2. Superconductivity of Metals and Alloys by P. G. De Gennes
3. Introduction to Superconductivity by M. Tinkham
4. QuantumTheoryof Magnetismby R.M.White
5. The theory of Magnetismby D. C. Mattis

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in density functional theory, with the aim to build their background for future research work in this area.

Syllabus:

• Many-body problem: QM of electrons and nuclei, approximation methods for many electron systems, Born-Oppenheimer approximation, Hartree and HF theory, tight binding method, greens functions, electron correlation, Ci & many-body and Moller-plesset theory, complete active space methods, coupled cluster theory, density matrices, time-dependent approach to all the above formalism
• Foundations of Density Functional Theory(DFT): Hohenberg-Kohn (HK) theo-rem, degenerate ground states, variational DFT, N − and v− representability problem, Levy-Lieb constrained search, fractional particle number & derivative discontinuity, spin polarized systems, Exited states part i: Effective Single particle picture: Kohn-Sham (KS) construction, non-interacting v− representability, degenerate KS DFT, KS equations forspin polarized systems, interpretation of KS eigenvalues
• Exchange-Correlation (XC) Energy Functional: exact exchange formalism within DFT, exact representations of the energy functional, LDa, gga, meta-gga, weighted density approximation, self interaction correction (SiC), virial theorems, exact exchange formalism (OpM, KLi, HS), where DFT goes wrong, strengths of DFT, strong correlation: DFT+U, Rpa, gW, DFpT, DMFT, orbital free DFT, DFT- hybrid
• Crossover to Excited-States: time-dependent DFT: Runge-gross theorem, time- dependent KS equations, adiabatic LDa & TD XC potentials, linear response TDDFT, Excited states part ii, spin polarized TDDFT, frequency dependent XC kernel, TDCDFT, TDOEp, relativistic DFT, molecular orbital theories

Reference Book

1. Density Functional Theory of atoms and Molecules by Robert G. Parr and Weitao Yang
2. Density functional Theory by R.M. Dreizler and E.K.U. Gross
3. Density Functional Theory by Eberhard Engel
4. Primer in Density Functional Theory by C. Fiolhais, F. nogueira, Miguel and A. L. Marques
5. Fundamentals of TDDFT by Miguel A. L. Marques et al.
6. Time-dependent Density Functional Theory by Miguel A. L. Marques et al.
7. Time-dependent Density Functional Theory by Carsten Ullrich
8. Quantal Density Functional Theory I & II by Viraht Shani
9. Recent advances in Density Functional Methods (Part I, II & III) by Delano P Chong
10. Atomic and Electronic Structure of Solids by Ethimios Kaxiras
11. Electronic Structure: Basic Theory and Practical Methods by Richard M. Martin
12. Many-Body Quantum Theory in Condensed Matter Physics by H. Bruus and K. Flensberg
13. Quantum Theory of the Electron Liquid by Gabriele Giuliani and Giovanni Vignale
14. Molecular Electronic Structure Theory by T. U. Helgaker, P. Jorgensen and J. Olsen
15. Electronic Structure Calculations for Solids and Molecules by J. Kohanoff
16. Methods of Electronic Structure Calculations by M. Springborg
17. Self Consistent Fields in Atoms by Norman March
18. Computational Materials Science by J. G. Lee
19. Density Functional Theory in Quantum Chemistry by Takao Tsuneda
20. Material Modeling using DFT by Feliciano Giustino

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in advanced quantum field theory, with the aim to build their background for future research work in this area.

Syllabus:

• Path-integral formulation of quantum mechanics
• Path-integral for scalar fields, generating functional, connected Greens functions, Feynman rules, 1 loop diagrams
• Grassmann variable, path-integral for Dirac field
• Path-integral for Electromagnetic field, gauge fixing
• QED, symmetries and Ward identity
• Renormalization divergences and power counting, Φ4 theory, QED, spontaneous symmetry breaking, Renormalization group basics (running of coupling).
• Yang-Mills theory, gauge fixing and ghosts, BRST, asymptotic freedom

Reference Book

1. An Introduction to Quantum Field Theory by M. Peskin and D. V. Schroeder
2. Quantum Field theory:From Operators to Path Integrals, 2nd edition by Kerson Huang
3. Quantum Field Theory by Mark Srednicki
4. Quantum Field Theory by Claude Itzykson and Jean Bernard Zuber
5. Notes from Sidney Coleman's Physics 253a, arXiv: 1110.5013

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in quantum information and computation, with the aim to build their background for future research work in this area.

Syllabus:

• Introduction to Classical information: Shannon entropy, Mutual Information
• Quantum Information I: Hilbert space, density matrices, quantum entropy and Holevo bound
• Quantum Information II: Entanglement, Teleportation, super dense coding & Bell inequalities
• Quantum dynamics:Two level systems, decoherence and Rabi oscillations
• Quantum computation: single qubit gates-phase, swap, Hadamard, two qubit gates-CNOT
• Quantum algorithms: Deutsch, Grover, Introduction to Shor’s algorithm
• Quantum error correction
• Applications: Quantum simulation and Adiabatic quantum computation
• Solid state quantum information & computation: Introduction to entanglement in nanostructures, quantum computation with superconducting devices and topological quantum computation

Reference Book

1. Introduction to Quantum Information Science by V. Vedral (Oxford U. Press)
2. Quantum Information & Computation by M. A. Nielsen & I. L. Chuang (Cambridge U. Press)
3. An Introduction to quantum computing Kaye by P. R. Laflamme and A. M. Mosca (Oxford U. press)

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in experimental high energy physics, with the aim to build their background for future research work in this area.

Syllabus:

• The interaction of high-energy particles with matter: specific applications related to EHEP. Relativistic kinematics: Detailed derivation of kinematic variables and their transformations whenever needed. Decay kinematics. Rapidity, pseudo-rapidity, space-like and time-like. Some examples where relativistic kinematics play important role for understanding of data.
• Detectors in High Energy physics: general concept of building a HEp experiment, coverage and option
• Gas detectors; Semiconductor detector; Scintillator and Cerenkov detectors Specific to EHEP
• Calorimeter and Pre-shower detectors: principle of electromagnetic and hadronic shower generation. Detector Simulation: need of simulation, various techniques, MC, some general
• Concepts. Data analysis in HEp: general approach of data cleanup, calibration, track reconstruction, reconstruction of events Error analysis in EHEp. Computing in EHEp: Basics of OO programming using C++, few applications in EHEpdata analysis.

Reference Book

1. Relativistic Kinematics; a guide to the kinematic problems of High Energy physics by R.Hagedorn
2. The Experimental Foundations of particle physics by R. N.Cahn and G. Goldhaber
3. Techniques for nuclear and particle physics experiments: a How to approach by W. R.Leo (Springer)
4. Experimental Techniques in Hugh Energy Nuclear and Particle physics by T. Ferbel (WorldScientific)
5. Introduction to Experimental particle physics by R. C. Fernow
6. Data Reduction and Error analysis for the physical sciences by P.Bevington and D. K. Robinson
7. Data analysis Techniques for High Energy physics by R. Frunwirth, M. Regler, R. K. Bock and H. Grote

Course: UG-Elective

Approval: 42 Lectures + 14 Tutorias

Credit: 8

Outcome:
This course teaches the students important concepts and methods in experimental techniques, with the aim to build their background for future research work in this area.

Syllabus:

• Mechanical drawing and designs: Mechanical drawing tools, basic principles of mechanical drawing, dimensions, tolerances, from design to working drawings.
• Basics tools: hand tools, machines for making holes, lathe & milling machines, grinders, casting
• Vacuum technology: gases, gas flow, pressure and flow measurement, vacuum pumps, pumping mechanisms, ultrahigh vacuum, leak detection
• Optical systems: optical components, optical materials, optical sources
• Charge particle optics: electrostatic lenses, charged-particle sources, energy and mass analyzer
• Detectors: optical detectors, photoemission detectors, particle and ionizing radiation detectors, signal to noise ration detection, surface barrier detector, Particle detector: interactions of charged particles and photons with matter; gaseous ionization detectors, scintillation counter, solid state detectors
• Electronics: electronic noise, survey of analog and digital I/Cs, signal processing, data acquisition and control systems, data analysis evaluation
• Nano- and micro-fabrication: various lithography techniques such as photolithography, nanoimprint lithography, e-beam lithography, ion-ball milling
• SEM, TEM, X-ray diffraction, SQUID Magnetometry, Magnetotransport, PL/CL time resolved spectroscopy, Rutherford Backscattering spectrometry (RBS), RBS-Channeling, UV-ViS-iR spectrometry.

Reference Book

1. The art of Measurement, by Bernhard Kramer (V. C. H. Publication)
2. Building Scientific Apparatus by J. H. Moore et al.
3. Experiments in Modern Physics, Second Edition by Adrian C. Melissinos and Jim Napolitano
4. The art of Experimental Physics by Daryl W. Preston
5. Vacuum Technology by A.Roth (North-Holland publisher)
6. Charge particle Beams by Stanley Humphries (John Wiley and Sons)
7. Principles of Charged Particles Acceleration, by Stanley Humphries (John Wiley and Sons)
8. Radiation Detection and Measurements by G. Knoll (3rd Edition)
9. Techniques for Nuclear and Particles Physics Experiments by W.R. Leo (2nd edition, Springer)

Course: UG-Elective, PG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches the students important concepts and methods in introductory cosmology, with the aim to build their background for future research work in this area.

Syllabus:

• The cosmic history and inventory
• A sketch of general Relativity.
• The expanding Universe
• Friedmann Equations and Cosmological Models
• The Standard cosmological model.
• The inflationary Universe.
• Primordial nucleosynthesis and the thermal history of the Universe.
• Perturbations in an expanding Universe.
• Growth of perturbations
• Dark Matter Halos.
• Statistical description of gravitational clusteing.
• Special Topics: Fluctuations in the CMB, Lensing, Cluster Cosmology, The Lyman-alpha Forest, Reionization, Halo Model, Redshift Space Distortions.

Reference Book

1. Introducing Einstein’s General Relativity by Ray D’inverno
2. The Early Universe by E. W. Kolb andM.  S. Turner
3. Introduction to Cosmology by BarbaraRyden
4. Modern Cosmology by ScottDodelson
5. Principles of Physical Cosmology by P. J. E. Peebles
6. Large Scale Structure of the Universe by P. J. E.Peebles
7. Structure Formation in the Universe by T.Padmanabhan

Course: UG-Elective, PG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course provides the basic background for relativistic nuclear scattering processes and physics of quark gluon plasma.

Syllabus:

• Introduction to high energy heavy ion collisions and Quark-Gluon-Plasma, comparison of big bang and the little bang
• Thermodynamics: Relativistic gas (hadrons, quarks and gluons) and its statistical and thermodynamical properties, MIT Bag model, Hagedorn gas, phase diagram of QCD
• Relativistic Kinematics: four vectors notation, rapidity variables, pseudo rapidity variables, light cone variables, relativistic invariants, Dalitz plot, cross sections
• Collision Dynamics: initial state of nuclear collisions, fluid dynamical evolution, kinetic transport model, freeze-out and particle production
• Experiments: a general overview of different experimental setup related to search for QGP and relevant observables
• Signatures of QGP: collective flow, J/Ψ suppression, strangeness enhancement, jet quenching, electromagnetic probes, Hanbury-Brown-Twiss measurement
• Recent progress

Reference Book

1. Hadrons and QGP by Letterssier and Rafelski
2. Introduction to High Energy Heavy Ion Collissions by C. Y. Wong
3. Phenomenology of Ultra Relativistic Heavy Ion Collissions by W Florkowski
4. Ultra relativistic heavy ion collisions by R. Vogt
5. Introduction to relativistic heavy ion collisions, by L. P. Csernai
6. A Short Course On Relativistic Heavy Ion Collission by A. K. Chaudhuri
7. Extreme states of matter in strong interaction physics by Helmut Satz
8. Relativistic Hydrodynamics by L. Rezzolla and O. Zanotti
9. Finite Temperature Field Theory by J. I. Kapusta and C. Gale
10. The Early Universe by Kolb and Turner
11. Fantastic Realitis by Frank Wilczek
12. Research Reports in Physics, Quark Gluon Plasma, Invited lectures of Winter School, Published by Springer Verlag, Editors - B. Sinha, S. Pal and S. Raha
13. The Physics of Quark Gluon Plasma, Introductory lectures, Lecture Notes in Physics 785, Publisher - Springer, Editor - S. Sarkar, H. Satz and B. Sinha
14. Quark Gluon Plasma - From big bang to little bang, K. Yagi, T. Hatsuda, Y. Miake, Cam- bridge Monograms on Particle Physics, Nuclear Physics and Cosmology
15. Quark Gluon Plasma: Theoretical Foundations, An annotated reprint collection - J. Ka- pusta, B. Muller and J. Rafelski, Publisher - Elsevier Science

Course: UG-Elective, PG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course provides the basic background of non-equilibrium statistical mechanics and out of equilibrium dynamics.

Syllabus:

• Kinetic theory of gases, Bolzmann distribution and its implications.
• Bolzmann equation, H Theorem, Conservations laws and Hydrodynamics
• Linear response, fluctuation dissipation theorem,Green-Kubo formula
• Markov Processes: Conditional probabilities, Markov processes, Chapman-Kolmogorov equation, Master equation, Fokker Planck equation, Random walk processes,Ising Glauber Model
• Stochastic differential equations: Langevin equation, stochastic integration, Ito calculus, Stratonvich integrals
• Diffusion equations, first passage problems, driven diffusive systems
• Applications: Aggregation,Fragmentation,Phase ordering Kinetic,Exclusion processes

Reference Book

1. Stochastic Methods by C. Gardiner
2. A Kinetic View of Statistical Physics by P. L. Kaprivsky, S. Redner and E. Ben Naim
3. Statistical Physics 2- Nonequilibrium Statistical Mechanics by R. Kubo, M. Toda and N. Hashitsume
4. Stochastic Processes in Physics and Chemistry by N. G. Van Kampen.
5. Theory and Applications of Stochastic Processes by Z. Schuss
6. A Guide to First Passage Processes by S. Redner

Course: UG-Elective, PG-Elective

Approval: 42 Lectures + 14 Tutorials

Credit: 8

Outcome:
This course teaches advanced topics in quantum mechanics which provides the much needed background in concepts and technique in present day research in interface of the area of quantum mechanics, many body physics and information theory.

Syllabus:

PART I: Quantum entanglement & applications:

• Density matrices
• Tensor product and entangled states coherent and squeezed states; Bell basis
• Quantum teleportation
• EPR and Bells inequalities
• Shannon entropy: Qbits, introduction to quantum computing principles; measurement and decoherence

PART II: Introduction to many particle QM:

• Creation/ Annihilation operators; Symmetization/Antisymertization; many body operators, Boson/Fermion coherent states, Grassmann algebra and Gaussian integrals using coherent states.
• Dynamical variables and dynamics of identical particles
• Applications to many body systems: Angular momentum of system of identical particles, first order perturbation in many body systems, introduction to Hartree-Fock methods.

PART III: Symmetries in QM

• Group representation, Point group symmetry, Lie Groups; Schur lemma, orthogonality theorems, irreducible representations, accidental degeneracies; Irreducible tensor operators and direct product representations, Wigner Eckart theorem
• Applications including molecular orbitals, space time symmetries of Bloch states; normal model of vibrations; characters of angular momentum states; SU(2), SU(3) representations

Reference Book

1. Part-I
2. Entangled systems by Jurgen Audretsch
3. Density Matrix Theory and Applications by Karl Blum
4. Quantum Mechanics by Leonard Susskind
5. Modern Quantum Mechanics by J. J Sakurai
6. Part-II
7. Quantum Mechanics Merzbacher (Chapters 21 and 22)
8. Quantum many particle systems J. W. Negele and H. Orland (Chapter 1)
9. Quantum Mechanics Schiff (Chapter 14)
10. Elements of Advanced Quantum Theory by J. M. Ziman (Chapters 1,2 and 5)
11. Modern Quantum Mechanics by J. J Sakurai
12. Part-III
13. Group Theory by M Tinkham
14. Group Theory by Hamermesh
15. Lie Algebras in Particle Physics: from Isospin To Unified Theories by Howard Geogie
16. Group theory and Chemistry by Bishop
17. Topics in Condensed Matter Theory by Michele Cini
18. Elements of Advanced Quantum Theory by J. M. Ziman (chapter 7)
19. Solid State Physics by Ashcroft and Mermin