Statistical Physics (2023)

Administrivia

Time: Tu, Th at 1130 hrs

Venue: AG 69

First lecture: 17 Jan

Credit policy: TBD

Instructor: Basudeb Dasgupta

Tutors: Rupak Majumdar and Asikur Rahman

Course Webpage: Moodle Link [TIFR only]

Lecture Notes: Dropbox Link [Public]

Course Contents

1. Preliminaries: Motivation and review of thermodynamics

2. Probability and statistics: Counting, distributions, large numbers

3. Kinetic theory and approach to equilibrium; Brownian walks etc.

4. Classical statistical mechanics: Formalism and simple systems

5. Classical statistical mechanics: Interactions, approximations, phase transitions

6. Quantum statistical mechanics: Formalism, ideal Bose/Fermi gases, phase transitions

7. What else is there? and Review of the course

References

1. Statistical Mechanics, Huang (I personally find it most readable)

2. Statistical Physics (Berkeley Physics Course Vol.5), Reif

3. Statistical Mechanics of Particles, Kardar (Main text, but very terse. Videos are awesome.)

4. Statistical Mechanics Part-I (Course of Theoretical Physics Vol.5), Landau and Lifshitz

5. Lecture notes by David Tong, Cambridge Univ. (Kinetic Theory, Statistical Mechanics)

Problem Sets

1. PS1 (thermodynamics and probability)

2. PS2 (kinetic theory)

3. PS3 (classical stat. mech + interactions)

4. PS4 (quantum stat. mech) due by 27 May

Exams

1. Droptest on 4 Feb (10-12)

2. Midterm (26th March)

3. Endterm (27 May)

Lecture Summaries

• Orientation (17 Jan)

 Lecture 1 (19 Jan)

• Why Statistical Mechanics? 

• Introduction to Thermodynamics

• Basic notions / terms used in Thermodynamics

Lecture 2 (24 Jan)

• Zeroth Law

• First Law

Lecture 3 (31 Jan)

• Second Law

Lecture 4 (2 Feb)

• Potentials

• Third Law

Droptest (4 Feb)

Lecture 5 (7 Feb)

• Probability

• Bayesian and Frequentist

Lecture 6 (9 Feb)

• Moments, Cumulants, and Generating Functions

• Many Random Variables

Lecture 7 (14 Feb)

• Central Limit Theorem for iids; and extensions

Lecture 8 (16 Feb)

• Summing large exponentials, Saddle point, Stirling's approximation

• Information Entropy

Lecture 9 (21 Feb)

• Phase space and Liouville eq.

• Equilibrium and its features

Lecture 10 (23 Feb)

• Liouville to BBGKY for dilute gas

• N particle density

• Time-scales

Lecture 11 (28 Feb)

• BBGKY to Boltzmann

• Coarse-graining and molecular chaos

Lecture 12 (2 Mar)

• Boltzmann eq. and local equilibrium

• H Theorem

Lecture 13 (7 Mar)

• Boltzmann eq. to Hydrodynamics via moments

Lecture 14 (9 Mar)

• Hydrodynamics at zeroth order: Waves

• First order: Diffusion

• Approach to global equilibrium and relevant timescales

Lecture 15 (14 Mar)

• Stochastic processes I (Guest lecture by Prof. Shamik Gupta)

Lecture 16 (16 Mar)

• Stochastic processes II (Guest lecture by Prof. Shamik Gupta)

Lecture 17 (21 Mar)

• Equilibrium

• Time average vs Phase average

• Main goal of Stat Mech : Assign probability to microstates

Lecture 18 (21 Mar)

• Microcanonical ensemble

• Density/Number of states

• Derivations of 0th, 1st, 2nd Laws of Thermodynamics

Midterm (26 Mar)

• Closed book. 1 A4 formula-sheet allowed.

• 2-5pm

Lecture 19 (28 Mar)

• Microcanonical Examples

Lecture 20 (20 Mar)

• Canonical and Examples

Lecture 21 (4 Apr)

• Grand Canonical and Examples

Lectures 22-26 (6, 18, 20, 25, 27 Apr)

• Classical Stat Mech. of Interacting Systems

• Mayer cluster expansion technique

• Mean Field Theory of Condensation

• 1st order Phase Transition

• Gibbs Canonical Ensemble and Multiple Saddle Points

• Meaning of Maxwell Construction

• Curie-Weiss Mean Field Theory

• 2nd Order Phase Transition

• Important Results on Phase Transitions (without proof)

Lectures 27-34 (2, 4, 6, 9, 11, 13, 16, 18 May)

• Discreteness of energy

• C_V of diatomic gas vs T

• C_V of a crystal and Debye's T^3 Law

• Black body radiation

• Symmetrization and Antisymmetrization

• Density matrix in energy and position bases

• Virial expansion and "effective potential" for ideal quantum gas

• Ideal quantum gas at high T (mu vs T, virial expansion again)

• Ideal Fermi gas (Fermi energy, mu, C_V, degeneracy pressure)

• Ideal Bose gas (BEC, pressure, C_V, mu)

Endterm (27 May)

• Closed book, A4 formula sheet allowed (both sides if needed)

• 2-5 PM in AG 69

• All assignments due before exam