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 Books

• Theoryof Superconductivityby J. R. Schrieffer

• Superconductivity of Metals and Alloys by P. G. De Gennes

• Introduction to Superconductivity by M. Tinkham

• QuantumTheoryof Magnetismby R.M.White

• The theory of Magnetismby D. C. Mattis

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 Books: 

• Principles of Quantum Computation and Information by G. Benenti, G. Casati, D. Rossini and G. Strini (Main Reference)

• Lecture notes on Quantum information and computation by J. Preskill (Supporting material)

Other useful Books

• Introduction to Quantum Information Science by V. Vedral (Oxford U. Press)

• Quantum Information & Computation by M. A. Nielsen & I. L. Chuang (Cambridge U. Press)

• An Introduction to quantum computing Kaye by P. R. Laflamme and A. M. Mosca (Oxford U. press)

Experiments 

•                     Study of magneto-resistance and its temperature dependence 

•                     Hall Effect (measurement of hall coefficient):

•                     Resistivity and determination of band gap measurement of semiconductor by Four- Probe method

•                     Solar Cell (IV characteristics)

•                     LC circuits (Simulating lattice dynamics for monoatomic and diatomic chains in 1 dimensions)

Experiments:

•         Motion of a freely falling body, 

•                     Measuring the value of g by compound pendulum

•                     Young’s modulus by bending of beam

•                     Study of soft massive spring, 

•                     Measuring specific heat of graphite, 

•                     Thermal conductivity of a bad conductor using Lee’s Method, 

•                     Latent heat of fusion of ice by using calorimetry, 

•                     Liquid drops formed under a plane surface, 

•                     Velocity of sound by Kundt’s tube, 

•                     Viscosity using a falling ball viscometer, 

•                     Reversible Pendulum, 

•                     Surface tension of fluids

Syllabus

• Monte Carlo: Markov chain, Metropolis algorithm, Ising Model, Determinantal Quantum Monte Carlo        

•  Molecular Dynamics: integration methods  extended ensembles, molecular systems

• Variational methods for Schroedinger Equation: Hartree-Fock methods.                                     

• Random phase approximations / time dependent Hartree-Fock approach                    

• Configuration interaction, coupled cluster methods, dynamical mean field theory                           

• Quantum molecular dynamics: Carr-Parinello approach

Reference Books:

• Computational Physics by Joseph Marie Thijssen, Cambridge University Press

• An Introduction to Computational Physics by Tao Pang, Cambridge University press

• Computer Simulation of Liquid by M. P. Allen and D. J. Tildesley, Clarendon press

• A Guide to Monte Carlo Simulations in Statistical Physics by L. Landau and K. Binder

• Quantum Monte Carlo Methods by M. Suzuki (Editor) Springer-Verlag

• New Methods in Computational Quantum Mechanics by I. Prigogine and Stuart A. Rice

• Understanding Molecular Simulation by D. Frankel and B. Smit, Second edition, academic press.

• Computational Methods in Field Theory by H. Gausterer and C.B. Lang

• F. Jensen, introduction to Computational Chemistry by F. Jensen

• Essentials of Computational Chemistry by C. J. Crammer

• Dynamical mean field theory by Jean-Marc Robin

• Quantum Monte Carlo Methods by James Gubernatis, Naoki Kawashima, Philipp Werner

• Computer Simulations using Particles - R. W. Hockney and J. W. Eastwood

Syllabus: 

1. Second Quantization, One and two body operators

2. Observables and their relationship to one and two body Greens functions

3. Thermodynamic potential, Spectral functions, Analytic properties of Greens function

4. Linear Response, correlation function, sum rules

5. Canonical Transformation – Bogoliubov Valetin, Schrieffer Wolf etc.

6. Equation of motion

7. Diagrammatic Perturbation theory for Green function and thermodynamic potential, Luttinger Ward Identities

8. Mean field theory

9. Functional Integration Methods

Reference Books: 

1. Landau Lifshitz Statistical Physics Part II

2. Greens function for condensed Matter by Rickeyzen

3. Greens function for condensed Matter by Doniach and Sondhaimer

4. Quantum Theory of Many body Particle systems by Fetter Walecka

5. Many Particle Physics by Ben Simon

6. Basic Notions in Condensed Matter by P.W. Anderson

7. Techniques and application of Path-integration Plan by S. Schulman 

Syllabus: 

1. Hilbert space formalism for quantum mechanics

2. Review of time independent perturbation theory, WKB approximation, bound state perturbation theory

3. Time-dependent perturbation theory, scattering theory

4. Greens function methods, Path integral in non-relativistic theory

5. Relativistic wave equations – Dirac Equation, Dirac particle in presence of an electromagnetic field leading to g = 2, holes

6. Foundational issues in quantum theory

Reference Books: 

1. Modern & Advanced Quantum Mechanics by J. Sakurai

2. Principles of Quantum Mechanics by R. Shankar

3. Quantum Mechanics by by Merzbacher

4. Quantum Mechanics (volumes 1 and 2) by A. Messiah

5. Quantum Mechanics by Cohen- Tannoudji

                 Syllabus

1. 1. 1. HIlbert space (states, operators, evolution)

      2. One dimensional problems & Harmonic oscillator, delta & periodic pots

      3. Bound states vs scattering states

      4. The central force problem

      5. The hydrogen atom, hard and soft sphere

      6. Time-independent perturbation theory, WKB approximation, variational method

      7. Time-dependent perturbation theory, Heisenberg and interaction represtations

      8. Dirac equation, Scattering theory/semi classical theory of radiation/identical particles/ angular momentum/ path integrals(depending of available time).

       Reference Books:      

1. 1. 1. R. Sankar-principles of Quantum Mechanics

      2. Cohen-Tannoudji, Diu and Laloe- Quantum Mechanics I & II

      3. J.J Sakurai-Modem Quantum mechanics

      4. David Griffiths-Intruduction to Quantum mechanics

      5. Eugen Merzbacher-Quantum mechanics

      6. Bransden and joachain-Quantum mechanics

      7. Quantum mechanics - L. I. Schiff