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