Teaching

Physics of Waves (PH11003), Spring, 2023–2024

Condensed Matter Physics II (PH41017), Autumn, 2021-22

Computational Methods (PH41012), Spring, 2020-21

Statistical Physics II (PH51023), Autumn, 2020

Mathematical Methods II [PH41008], Spring, 2019-20

Course webpage (may not work): piazza.com/iitkgp.ac.in/spring2020/ph41008/home

General outline of the course
Part 0
Fourier transform. Ordinary differential equations. Greens functions.
Part IA
Partial differential equations (PDE) in Physics: preliminaries; first-order PDEs; classification of second-order quasilinear equations; elliptic, hyperbolic and parabolic type; characteristics; boundary conditions and types of equations.
Part IB
One-dimensional wave equation; one-dimensional diffusion equation; the two dimensional Laplace equation; Green’s function for PDE; singular part of the Green’s function for PDE with constant coefficients;
Part IC
Possion’s equation; the diffusion equation; the wave equation; Dirichlet and Neumann problems; the initial value problem for the wave equation; the method of images; the method of separation of variables; 3D Laplace equation in spherical polar coordinates; associated Legendre functions and spherical harmonics. Part ID Numerical solutions. Distribution theory.
Part II
Group Theory: definitions and nomenclature; examples; rearrangement theorem; cyclic groups; subgroups and cosets; Cayleys theorem and Lagranges theorem; conjugate elements and class structure; factor groups; isomorphy and homomorphy; direct product groups; symmetric groups.
Part III
Representation of finite groups; definition ; unitary representation; Schurs Lemma; orthogonality theorem; reducible and irreducible representations; characters; regular representation; product representation; character table; examples of S3 and C4v; introduction to Lie groups and Lie algebra; Clebsch- Gordon coefficients.

Reference books:

  • Mathematical Methods for Physics and Engineering. K. F. Riley, M. P. Hobson, and S. J. Bence. Cambridge University Press. (Lower bound for the course)
  • Mathematical Physics: A Modern Introduction to Its Foundations. S. Hassani. Third edition 2002. Springer. (Quite formal)
  • Methods of Mathematical Physics Volume II. R Courant and D. Hilbert. (Very extensive)
  • Differential Equations. H. T. H. Piaggio. (Occasional reference)
  • Contemporary Abstract Algebra. J. A. Gallion. Cengage/Narosa.
  • Lie Algebra in Particle Physics. G. Howard. Second Edition 2009.

Statistical Physics II [PH51023 ]

Autumn Semester 2019

General outline of the course
Part 0
Quick summary: Different kinds of ensembles. Application to non-interacting systems.
Part IA
Phase transitions: Examples; general concepts; models; analytic properties of models; Mean-field theories (MFT): Magnetic and fluid systems. (i) Weiss MFT; (ii) Brag-Williams MFT; (iii) Van der Waals theory.
Part IB
Critical phenomena: long-range order, order parameter, scaling, universality and critical exponents. Landau theory of phase transitions (LTPT). Extension to inhomogeneous systems. Role of fluctuations and break-down of LTPT. Gaussian approximation.
Part IC
Introduction to renormalization group (RG) method to study continuous phase transitions. Examples. Real-space RG and Momentum-space RG.
Part ID
Phase transitions on low-dimensional systems. Mermin-Wagner theorem. Topological phase transitions.
Part II
Macroscopic quantum phenomenon: Superfluidity. Mean-field level description. Condensate wave function. Off-diagonal-long-range-order (ODLRO). Properties of superfluid flow.
Part III
Elements of non-equilibrium statistical physics: Noise and stochastic processes. Brownian motion. Diffusion. Einstein relation. Fluctuation and dissipation.

References

There are many excellent textbooks. Any single book will not suffice for all your needs, still some will come close to it. Also you will have to search for the one that you will enjoy reading and some you will simply abhor.

♠ Suitable for first course on Statistical Mechanics

  • F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw Hill, 1965.
  • D.J. Amit and Y. Verbin, Statistical Physics: An Introductory Course, World Scientific, 1999.
  • J.P. Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity, Oxford University Press, 2006.
  • J.K. Bhattacharjee, Statistical Mechanics An Introductory Text, Allied Publishers, India, 2002.
  • M. Kardar, Statistical Physics of Particles, Cambridge University Press, UK, 2007.

♠ ————————Intermediate level ————————————–

♠ Phase transitions and much more

  • R. K. Pathria. Statistical Mechanics, Second Edition, Elsevier.
  • M. Plischke and B. Bergersen, Equilibrium Statistical Mechanics, Sec- ond Edition (World Scientific, Singapore, 2003).
  • C.J. Thompson, Classical Equilibrium Statistical Methods Springer- Verlag (1988).
  • S. K. Ma. Modern Theory Of Critical Phenomena.
  • L.P. Kadanoff, Statistical Physics: Statics, Dynamics, and Renormal- ization (World Scientific, Singapore, 2000).
  • J.M. Yeoman, Statistical Mechanics of Phase Transitions, Clarendon Press, Oxford (1992).
  • H.E. Stanley, Introduction to Phase Transitions and Critical Phenom- ena, Clarendon Press, Oxford (1971).
  • R.J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, London, 1982.
  • Editors, C. Domb and M.S. Green, Phase Transitions and Critical Phe- nomena Vols. 1-6, Academic Press. Also, C. Domb and J. Lebowitz, Vols. 7-20. (Search on Internet for details about full series.)
  • P A M Chaikin and T. C. Lubensky. Principles of Condensed Matter Physics, Cambridge University Press.
  • Nigel Goldenfeld. Lectures on Phase Transitions and the Renormalisa- tion Group, (Levant Books, Kolkata, 2005).
  • M. Kardar, Statistical Physics of Fields (Cambridge University Press, UK, 2007).
  • L. D. Landau and E. M. Lifshitz. Statistical Physics, Pergamon, 1980.
  • C. Itzykson and J.-M. Drouffe, Statistical Field Theory, Vols. I and II, Cambridge University Press, 1989.
  • D. Forster. Hydrodynamic Fluctuations, Broken Symmetry, and Cor- relation Functions.

♠ Non-equilibrium statistical mechanics and much more

  • V. Balakrishnan, Elements of Nonequilibrium Statistical Mechanics, Ane Books, Pvt. Ltd., India, 2008.
  • J.K. Bhattacharjee and S. Bhattacharyya, Nonlinear Dynamics Near and Far from Equilibrium, Hindustan Book Agency, 2007.
  • M. Le Bellac, F. Mortessagne, and G.G. Batrouni, Equilibrium and Non-Equilibrium Statistical Thermodynamics, Cambridge University Press, 2010.
  • N. Pottier, Nonequilibrium Statistical Physics, Oxford University Press, 2010.
  • N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland ( 1985).
  • C.W. Gardiner, Handbook of Stochastic Methods, Springer-Verlag (1983).

♠ Numerical simulations

  • D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 3rd Edition, Cambridge University Press, 2013.
  • W. Krauth, Statistical Mechanics: Algorithms and Computations, Ox- ford University Press, 2006.
  • D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, 2001.
  • M.P. Allen and D.J. Tildesley Computer Simulation of Liquids, Oxford University Press, 1989.

♠ Advanced topics

  • S. Sachdev, Quantum Phase Transitions, Cambridge University Press, 1999.
  • A. Auerbach, Interacting Electrons and Quantum Magnetism, Springer, 1998.
  • D.R. Nelson, Defects and Geometry in Condensed Matter Physics, Cambridge University Press, 2002.