Statistical Mechanics

Statistical Mechanics (StatMec | INR7007U)

Description: The Methodology of Statistical Mechanics (5 lectures)

- Relationship between statistical mechanics and thermodynamics - emergence.

- Review of equilibrium statistical mechanics.

- The grand canonical ensemble. Chemical potential. The Bose and Fermi distribution functions.

- The classical limit, phase space, classical partition functions.

Weakly Interacting Systems (7 lectures)

- Non-ideal systems. The imperfect gas and the virial expansion, Mayer's f function and cluster integrals. (2 lectures)

- The second virial coefficient for the hard sphere, square-well and Lennard-Jones potentials. (2 lectures)

- Throttling and the Joule-Kelvin coefficient. (1 lecture)

- The van der Waals gas as a mean field paradigm. (2 lectures)

Strongly Interacting Systems (13 lectures)

- The phenomenology of phase transitions, definitions of critical exponents and critical amplitudes. (2 lectures)

- Scaling theory, corresponding states. (2 lectures)

- Introduction to the Ising model. Magnetic case, lattice gas and phase separation in alloys and Bragg-Williams approximation. Transfer matrix method in 1D. (3 lectures)

- Landau theory. Symmetry breaking. Distinction between second order and first order transitions. Discussion of ferroelectrics. (3 lectures)

- Broken symmetry, Goldstone bosons, fluctuations, scattering, Ornstein Zernike, soft modes. (3 lectures)

Dissipative Systems (5 lectures)

- Fluctuation-dissipation theorem, Brownian motion, Langevin equation, correlation functions. (5 lectures)

This module is taught by RHUL


Juno Champion

The school holds Juno Champion status, the highest award of this IoP scheme to recognise and reward departments that can demonstrate they have taken action to address the under-representation of women in university physics and to encourage better practice for both women and men.