Statistical Physics

• Express thermodynamic equilibrium conditions for isolated, closed, as well as open systems.
• Determine the number of microstates corresponding to a given macrostate in a wide spectrum of problems and establish the connection to thermodynamics through the entropy.
• Argue for the choice of appropriate statistical mechanical ensemble associated with a given problem and calculate physical properties by means of partition functions.
• Solve problems with non-interacting fermions, bosons, and quasiparticles (like photons).
• Describe important properties of the Ising-model in 1 and 2 dimensions.
• Employ mean-field models for describing phase transitions and properties of interacting systems.
• Estimate fluctuations in physical quantities, in particular in nanostructures.
• Discuss characteristics of phase transitions and apply Landau free energy expansions on continuous phase transitions.
• Simulate simple statistical mechanical systems on a computer

Thermodynamical equilibrium and state variables. Thermodynamic potentials. Number of microstates and entropy. Ensemble theory and mean values. Partition functions. Fluctuations in nanoscale systems. The microcanonical, the canonical, and the grand canonical ensembles. Spin-½ systems. Para- and ferromagnetism. Ising-models. The classical ideal gas. The equipartition law. Quantum statistics. The Maxwell-Boltzmann, the Fermi-Dirac, and the Bose-Einstein distributions. The Planck-distribution, Ultrarelativistic particles , photons, phonons. Classical gasses and liquids: Dealing with interacting particles. Phase transitions. Critical phenomena.

Lectures and exercises.