Statistical Physics (P602), Fall 2024
Instructor: Romain Vasseur, Associate Professor
office: Hasbrouck 405A
email: rvasseur[at]umass[dot]edu
office hours: by appointment and email, or visit my office
Lectures: MWF 12.20-13.10pm, room: Has 104A
TA: Sofia Corba
email: spcorba[at]umass[dot]edu
Textbook: Kardar, Statistical Physics of Particles (Cambridge University Press)
I also strongly recommend David Tong’s lecture notes: http://www.damtp.cam.ac.uk/user/tong/statphys.html
Website: https://websites.umass.edu/rvasseur/teaching/. Course materials will also be made available on Moodle.
Grading:
The course grade will be based 35% on the homework, 30% on the midterm, and 35% on the final exam.
Topics:
- Introduction and probabilities
- The fundamentals of statistical mechanics
- Classical ideal gases
- Thermodynamics
- Quantum statistical mechanics (phonons, photons, diatomic gases)
- Ideal Bose and Fermi gases
- Interacting systems and phase transitions
- Dilute interacting gases and van der Waals equation
- Phase transitions (Ising model, mean field theory, critical exponents)
- Landau theory
- Renormalization group
- Numerical methods
Lecture Notes:
- Introduction
- The fundamentals of statistical mechanics
- Ideal classical gases
- Thermodynamics
- Quantum Statistical Mechanics
- Ideal Bose and Fermi gases
- Interacting systems and phase transitions
- Numerical Methods
Combined file (87 pages): P602_Combined
Schedule:
- 9/5: Introduction, statistics and coin toss. (Chap 1)
- 9/6: Central limit theorem and Maxwell-Boltzmann distribution. (Chap 1)
- 9/6: afternoon: Microcanonical ensemble (Chap 2: pages 1-5)
- 9/9: Two-level systems, Pressure, Canonical ensemble. (Chap 2: pages 6-9)
- 9/16: Energy fluctuations in the canonical ensemble, equivalence of canonical and microcanonical ensembles. (Chap 2: pages 9-11)
- 9/18: Free energy, chemical potential and grand canonical ensemble. (Chap 2: pages 12-14)
- 9/23: Grand potential. Ideal gas: from quantum to classical (Chap 2: page 15. Chap 3: pages 1-2.)
- 9/25: Ideal monoatomic gases, free energy, equation of state, equipartition, Gibbs’ paradox. (Chap 3: pages 3-5.)
- 9/27: Ideal gases cont’d, chemical potential, diatomic gas and specific heat. (Chap 3: pages 5-7.)
- 9/27 afternoon: Ideal gases in the micro canonical ensemble. Quantum stat mech: density of states. (Chap 5: pages 1-2.)
- 9/30: Black body radiation (Chap 5: pages 2-4)
- 10/02: Phonons (Chap 5: pages 5-7)
- 10/07: Diatomic gas revisited, Bose-Einstein distribution (Chap 5: page 7, Chap 6: pages 1-2)
- 10/09: Bose gases: high T expansion (Chap 6: pages 2-4).
- 10/11: BE condensation (Chap 6: pages 4-5).
- 10/14: BE condensation (cont’d: 5-7).
- 10/16: end BEC. Fermi gases (Chap 6: pages 7-8)
- 10/18: Degenerate Fermi gas at T=0, Fermi energy. (Chap 6: pages 7-9)
- 10/21: Sommerfeld expansion. specific heat. (Chap 6: pages 9-11)
- 10/23: Pauli paramagnetism. (Chap 6: page 12)
- 10/25: Virial expansion (Chap 7: pages 1-2)
- 10/28: VdW equation of states (Chap 7: pages 3-4)
- 10/30: Maxwell construction, phase diagram, universality (Chap 7: pages 4-5)
- 11/1: Universality, Ising model (Chap 7: pages 5-6)
- 11/4: Ising model, mean-field theory
- 11/6: Mean-field theory cont’d, critical exponents and universality
- 11/8: Solution of the 1d Ising model, transfer matrix
- 11/13: Landau theory
- 11/15: Landau theory con’d
- 11/18: RG: general approach, 1d Ising model.
- 11/20: RG: Migdal-Kadanoff approximation