Statistical Physics module (PH51011)

​​You will be introduced to the basic theoretical tools used to understand the collective behaviour of large numbers of particles and connect microscopic physical models with macroscopic thermodynamic observables.

​The module begins with a review of thermodynamics and classical statistical mechanics. You will then learn about the black-body radiation and how to derive the famous Planck’s formula.

​The module will then move onto quantum statistics. Here, you will learn about Fermi-Dirac and Bose-Einstein distributions. You will study how they are used to explain phenomena such as the low temperature-dependence of the specific heat of metals and Bose-Einstein condensation.

​You will also study the thermodynamics of phase transitions and their classification. You will then focus on continuous phase transitions and discuss scaling hypothesis and the Landau's mean-field theory.

​Finally, we will cover basics of the out-of-equilibrium physics. This includes the Fick‘s law of diffusion, the Langevin equation, random walk and the Ornstein-Uhlenbeck process.

​What you will learn

​In this module, you will:

• ​review core thermodynamic concepts. These include state variables, thermodynamic potentials, and the laws of thermodynamics
• ​classical statistical mechanics and the micro-canonical, canonical, and grand-canonical ensembles
• ​black-body radiation, the failure of classical physics, and Planck's formula
• ​specific heat of solids through the Einstein and Debye models
• ​Fermi-Dirac statistics, Fermi energy, and the Sommerfeld expansion
• ​Bose-Einstein statistics and Bose-Einstein condensation
• ​thermodynamics of phase transitions, Ehrenfest classification, scaling theory, and Landau's mean-field theory
• ​fundamentals of out-of-equilibrium physics. These include the diffusion equation, random walk, the Langevin equation, Brownian motion, and Orstein-Uhlenbeck process

​By the end of this module, you will be able to:

• ​show familiarity with the concept of statistical ensembles. You will also be able to show connections between microscopic models and thermodynamics
• ​show basic understanding of quantum statistics, continuous phase transitions, and stochastic processes
• ​identify and apply appropriate high-level mathematical and physical techniques.

Assignments / assessment

• ​​Coursework assignments (20%)
  • ​These will be submitted throughout the module
• ​In-course midterm assessment (30%)
• ​Two-hour degree exam (50%)​

Teaching methods / timetable

• ​​seminars
• ​tutorials​

​​To take this module, you must have previously taken PH32009 Thermal Physics I​.