Department of Physics

18005  Statistical Physics     

Course Webpage: https://eclass.uoa.gr/courses/PHYS185

Course Content

• Phase space—statistical distributions; Introduction to phase space and statistical probability distributions. The concepts of a macro-state and of thermodynamic equilibrium.
• Microcanonical ensemble: Introduction to the microcanonical ensemble. The concept of statistical independence of systems. The concept of entropy and the law of entropy increase. The concept of temperature.
• Quantum statistical mechanics: The statistical density matrix. The quantum version of Liouville’s theorem.
• Canonical ensemble: The canonical ensemble. Calculation of thermodynamic quantities in the canonical ensemble. Examples. Distinguishable particles. Classical and quantum partition function.
• Simulations: The general idea about Monte Carlo simulations. The Metropolis algorithm. The molecular dynamics algorithm. Examples.
• Quantum gases: Identical particles. The statistical density matrix for free particles. The grand canonical ensemble. Statistical distributions for non-interacting bosons and fermions. Bose-Einstein condensation. Applications in liquid helium and ultracold gas condensates. Black body radiation.
• Thermodynamics of the solid body: Atomic vibrations. Classical and quantum treatment. Quantization of the elastic field. Phonons. Thermodynamics of phonons.
• Mean field theory—Ising model: The Ising model. Exact solution in one dimension. Mean field approximation. The Ising model in high dimensions. Exact solution in two dimensions.
• Critical phenomena: The concept of the order parameter. Universality and critical exponents. Landau-Ginzburg theory. Effective theory and the renormalization group. General methodology and conclusions. The role of large wavelengths. Scaling theory and the role of finite systems.
• Path integrals: Path integrals for many body systems following fermionic and bosonic statistics. Path integrals for spin systems.