Statistical Physics II (PH51023)

Semester: Autumn 2020

Syllabus, References and Grading policy

Prerequisite: Motivation and willingness to learn. Rest is secondary.

Review of elementary equilibrium statistical physics. Stochastic dynamics. Phase transitions. Low-dimensional systems. Macroscopic quantum phenomenon

Teaching Assistant: Sudip Das.

Lecture Notes

• Advanced Statistical Physics (Draft, evolving)
• Old personal notes: Brownian motion and Langevin Equation (Ref. R. K. Pathria, Statistical Mechanics, 2nd Ed.)
• Old personal notes: Master equation and Fokker-Planck Equation

Presentation Slides

• Introductory Remarks Date: 07/09/2020
• Ensembles: Microcanonical and Canonical Ensembles Date: 08/09/2020
• Brownian Motion, Random Walks and Diffusion Part IA Date: 14/09/2020
• Brownian Motion, Random Walks and Diffusion Part IB Date: 14/09/2020
• Brownian Motion, Random Walks and Diffusion Part II Date: 15/09/2020
• Stochastic Tools in Statistical Physics Part I Date: 21/09/2020
• Stochastic Tools in Statistical Physics (Notes) Date: 28/09/2020
• Stochastic Tools and Stochastic Processes Date: 29/09/2020
• Markov Processes, Master Equation, and Fokker-Planck Equation Date: 05/10/2020
• Correlation functions from Langevin formulation and Fokker-Planck Equation Date: 13/10/2020
• Smoluchowski Equation Date: 19/10/2020
• FPE. Phase Transitions Date: 20/102020

Video Lectures

• Introductory remarks
• Brownian motion, Random Walks and Diffusion I
• Brownian motion, Random Walks and Diffusion II (Langevin Equation)
• Stochastic Tools for Statistical Physics I

Useful Research Articles

Assignments

• Problem Set 1 Due date: October 01, 2020.
• Problem Set 2 Select problems from J.P. Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity, Oxford University Press, 2006.

Syllabus

Below is a tentative broad syllabus. Final syllabus would be decided based on the interests of the students and the instructor. It is highly likely that a largely truncated version of this syllabus would be followed.

Prerequisite: Motivation and willingness to learn. Rest is secondary.

Review of elementary equilibrium statistical physics. Ensembles. Application to non-interacting systems. Quantum statistics. 

(Suitable review material, references and a problem set would be provided.)

Stochastic dynamics: Review of notions of probability theory, Random walks and Brownian motion. Markov Processes. The Chapman-Kolmogorov equation. Master equation. Fokker-Planck equation. Exactly solvable systems. The Langevin approach. Diffusion. First-passage problems. Unstable systems. Kinetic models and Boltzmann equation. Irreversibiltiy. Stochastic differential equations. Additive and multiplicative noise. Numerical solution.

(No prerequisite assumed for this section.)

Phase transitions: Examples; general concepts; models; analytic properties of models; Mean-field theories (MFT): Magnetic and fluid systems.

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.

Introduction to renormalization group (RG) method to study continuous phase transitions. Examples. Monte Carlo and Molecular dynamics simulations.

Low-dimensional systems: Role of dimensionality and importance of fluctuations. Elementary ideas of Mermin-Wagner theorem and topological phase transitions.

Macroscopic quantum phenomenon: Superfluidity and Superconductivity. Mean-field level description. Condensate wave function. Off-diagonal-long-range-order (ODLRO). Properties of superfluid flow.

References:

(Below is a representative list. We will discuss about it later in the classroom.)

1. D.J. Amit and Y. Verbin, Statistical Physics: An Introductory Course, World Scientific, 1999.
2. J.P. Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity, Oxford University Press, 2006.
3. R. K. Pathria. Statistical Mechanics, Second Edition, Elsevier.
4. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Third Edition.
5. N. Pottier, Nonequilibrium Statistical Physics, Oxford University Press, 2010.
6. V. Balakrishnan, Elements of Nonequilibrium Statistical Mechanics, Ane Books, Pvt. Ltd., India, 2008.
7. J. F. Annett, Superconductivity, Superfluids and Condensates (Oxford Master Series in Physics), Oxford University Press (2004).
8. M. Kardar, Statistical Physics of Fields (Cambridge University Press, UK, 2007).

Grading Policy: 

Most probably continuous evaluation mechanism, as suggested by the Institute. 

Below is a tentative list of activities planned. It will be finalized later.

1. Participation in the (online) classroom activities; 
2. Assignments;
3. Quizzes; 
4. Three Tests (as recommended by the Institute); 
5. Mini projects/Term paper/Essay; 
6. Bonus marks problems. 

Freedom to choose your own topics. 

For any other information please feel free to contact me.