PH4211: Statistical Mechanics
“ Ludwig Boltzmann, who spent much of his life studying Statistical Mechanics, died in 1906,
by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our
turn to study Statistical Mechanics.
Perhaps it will be wise to approach the subject cautiously.”
in States of Matter, by David. L. Goodstein, 1975, Dover N.Y.
This is an advanced level course on Statistical and Thermal Physics; it builds on the
material learned by students in their first three years. The course starts with
a review of the formal structure of Statistical Mechanics and Thermodynamics considered
from a unified viewpoint. There is a brief revision of non-interacting systems. Following this the emphasis is on interacting
systems. First weakly interacting systems are considered, where the interest is in
seeing how such interactions cause small deviations from the non-interacting case. Following
this, systems are examined where interactions lead to drastic changes: namely phase
transitions. A number of specific examples is considered and these are unified within the
Landau theory of phase transitions. The final section of the course considers
non-equilibrium systems and the way these evolve towards equilibrium. Here fluctuations
play a vital role, understood in the context of Onsager's Regression Hypothesis, and formalised in the Fluctuation-Dissipation theorem.
2022 - The course runs on Tuesdays from 14:00 to 17:00 at Royal Holloway in Room T125 in the Tolansky building of the Physics department.
The course commences on Tuesday 18th January.
Revision Class 2022
Course Notes The the material is now available in book form - see Book List above. But a very drafty draft version of Edition 2 is available here.
Slides of individual week's lectures.
Video Panopto recordings of Chunks of lectures.
Interesting papers etc.
- Founders of thermodynamics and suicide.
- H. Eugene Stanley's calculation of the van der Waals critical parameters
- E. Cornell: Very Cold Indeed: The Nanokelvin Physics of Bose-Einstein Condensation - J. Res. Natl. Inst. Stand. Technol. 101, 419 (1996)
- W. Mullin: A New Derivation of the Virial Expansion - Am. J. Phys. 40, 1473 (1972)
- S. Brush: History of the Lenz-Ising Model - Rev. Mod. Phys. 39, 883 (1967)
- C. Wood: One hundred years of the Ising Model - Quanta Magazine June 20, (2020)
- D. Bitko: Quantum Critical Behaviour for a Model Magnet - Phys. Rev. Lett. 77, 940 (1996)
- J. Als-Nielsen and R. J. Birgeneau: Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions - Am. J. Phys. 45, 554 (1977)
- Brian J. Ford: Brownian Movement in Clarkia Pollen: A Reprise of the First Observations - The Microscope, 40 (4), 235 (1992)
- S. Braun et al.: Negative Absolute Temperatures for Motional Degrees of Freedom - Science 339, 52 (2013)
- A. J. Leggett: On the minimum entropy of a large system at low temperatures - Ann. Phys. 72, 80 (1972)
- S. Sachdev: Quantum Phase Transitions - Physics World, April (1999)
- S. Balibar: Qui a découvert la superfluidité? (Who discovered superfluidity?), January (2001)
- S. Balibar: The Discovery of Superfluidity - Journal of Low Temperature Physics, 146, 441-470 (1999)
- B. Cowan: On the Chemical Potential of Ideal Fermi and Bose Gases - Journal of Low Temperature Physics, 197, 412-444 (2019)
- M. Fisher: Scaling, universality and renormalization group theory - Stellenbosch Summer School 1982, 1-139 (1983)
- M. Fisher: The Nature of Critical Points - Boulder Summerr School 1964, 1-159 (1965)
- A. Sommerfeld: Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik
(On the electron theory of metals on the basis of Fermi's statistics) - Z. Phys. 47(1), 1-32 (1928)
Problem Assignments and Solutions
- Problems -- Numbered as in 2nd edition of course text book
- Solutions -- Numbered as in 2nd edition of course text book
Past Examination Papers
This page is still under construction; indeed it will continue so until the course is no longer taught!
Brian Cowan - E-mail: