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
- 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
