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Quantenstatistik Version Dez.23

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I) Concepts of probability

Random numbers, probabilities, simple rules; Mean values, standard deviation; Useful probability distributions; Random walk; Shannon’s entropy; Maximum uncertainty distributions; Central limit theorem.

II) Microstates in classical and quantum physics

Configuration, momentum, phase space; Phase-space measures; Liouville’s theorem; Microstates in quantum mechanics, density matrix, pure and mixed states; von Neumann’s theorem; Density of states; Ergodic hypothesis.

III) Statistical ensembles

Microcanonical ensemble, equilibrium, entropy, temperature, pressure, chemical potential; Canonical ensemble, Helmholtz free energy; Grandcanonical ensemble, grandcanonical potential.

IV) Classical gases

Ideal classical gas; Maxwell’s velocity distribution; Equipartition theorem; Diatomic molecular gases; Virial expansion; van der Waals equation.

V) Ideal quantum gases

Indistinguishable particles, fermions and bosons; Occupation numbers; Fermi-Dirac and Bose-Einstein statistics; Photon gas, black-body radiation; Phonon gas, atomic vibrations in solids; Bose-Einstein condensation; Degenerate Fermi gases, electrons in metals; Stability of stars*; Quantum gases at high temperatures, classical limit, Maxwell-Boltzmann’s statistics.

VI) Thermodynamics

Work in thermodynamic processes; First law of thermodynamics; Second law of thermodynamics; Free energies; Maxwell’s relations; Thermodynamics processes, Carnot’s efficiency; Conditions for thermodynamic equilibrium and stability; Gibbs-Duhem relation; Chemical reactions*.

VII) Emergent phenomena

Phase equilibria, Gibb’s phase rule; Phase transitions; Liquid-vapor phase-transitions in van der Waals gases*; Critical exponents; Landau’s mean-field theory of phase transitions; Ising model; Concept of renormalization group; Statistical physics models*, Computational methods*.

VIII) Advanced topics*

Thermodynamic fluctuations; Boltzmann equation; Linear response theory; Path integral formalism for statistical physics.