Statistical Physics (2024)

Administrivia

Time: Tu, Th at 930 hrs

Venue: AG 69

First lecture: 6 Feb

Credit policy: Tentatively Midterm (35%) + Endterm (35%) + Assignment (30%)

Instructor: Basudeb Dasgupta

Tutors: Sandeep Jangid and Soumya Pal

Course Webpage: Moodle [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)

Exams

1. Droptest on 18 Feb

2. Midterm (4 April, AG69)

3. Endterm (30 May, 9am-1pm, AG69)

Lecture Summaries (tentative)

 Lecture 1 (Feb 6)

• Why Statistical Mechanics? 

• Introduction to Thermodynamics

• Basic notions / terms used in Thermodynamics

Lecture 2 (Feb 8)

• Zeroth Law

• First Law

Lecture 3 (Feb 13)

• Second Law

• Potentials

• Third Law

Lecture 4 (Feb 15)

• Probability

• Bayesian and Frequentist

• Generating functions

Lecture 5 (20 Feb)

• Moments, Cumulants, and MGF, CGF, 

• Examples: Gaussian, Binomial

• Many Random Variables

Lecture 6 (Feb 22)

• Central Limit Theorem for iids; and extensions

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

Lecture 7 (Feb 27)

• Information and Entropy

Lecture 8 (Feb 29)

• Phase space and Liouville eq.

• Equilibrium and its features

Lecture 9 (Mar 5)

• Liouville to BBGKY for dilute gas

• N particle density

• Time-scales

Lecture 10 (Mar 7)

• BBGKY to Boltzmann

• Coarse-graining and molecular chaos

• Boltzmann eq. and local equilibrium

• H Theorem

Lecture 11 (Mar 12)

• Boltzmann eq. to Hydrodynamics via moments

• Hydrodynamics at zeroth order: Waves

Lecture 12 (Mar 14)

• First order: Diffusion

• Approach to global equilibrium and relevant timescales

Lecture 13 (Mar 19)

• Equilibrium

• Time average vs Phase average

• Main goal of Stat Mech : Assign probability to microstates

Lecture 14 (Mar 21)

• Density/Number of states

Lecture 15 (Mar 26)

• Microcanonical ensemble

• Microcanonical Example: Ideal gas

• Derivations of 0th, 1st Law

Lecture x (Mar 28)

• Lecture cancelled

Midterm Week (1-5 April)

• Midterm on 4th April

Lecture x (April 9)

• No class [Gudi Padwa]

Lecture x (April 11)

• No class [Eid ul Fitr]

Lecture 16, 17, 18, 19, 20 (April 16, 18, 23, 30, May 2)

• 2nd Law of Thermodynamics

• Canonical and Examples

• Grand Canonical and Examples

• 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 21, 22 (April 22 at 4pm, 25 at 10am)

• Stochastic Processes [Guest Lectures by Prof. Shamik Gupta]

Lectures 23 onwards (May 7, 9, 14, 16, 21, 23)

• 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)