Random physics

Alberto Verga, research notebook

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Work in progress

Lectures on Statistical Physics

Syllabus

Principles

  • Statistical ensemble: from the microscopic states to thermodynamics
  • Density matrix and the microcanonical distribution of an isolated system
  • Gibbs ensembles
  • Gibbs distribution (classical and quantum); the partition function and the free energy
  • Thermodynamic quantities

Noninteracting systems

  • Energy equipartition
  • Ideal gas
  • Rotation and vibration of molecules
  • Bose distribution, photons and phonons, Debye, Bose condensation
  • Fermi distribution, degenerated electron gas

Interactions

  • Pauli paramagnetism and mean field ferromagnetism
  • Landau diamagnetism
  • Ising model, low and high energy expansions in 2D
  • Cumulant expansion and virial coefficients
  • Van der Waals equation and liquid-gas transition

Phase transitions and fluctuations

  • Phenomenology and scaling laws
  • Order parameter and Landau free energy
  • Symmetry breaking
  • Linear response and correlations

Applications

  • From the binomial distribution to the large number and central limit theorems
  • Chaos, ergodicity and mixing
  • Mixing entropy and the Gibbs paradox
  • Maxwell demon and information theory
  • Two level systems
  • Quantum oscillator
  • Monte Carlo for the ising model
  • 2x2 random matrices, Wiener surmise
  • Lenard-Jones potential and molecular dynamics
  • White dwarf stars
  • Black hole entropy
  • Yang-Lee theory of phase transitions
  • Quantum spin in a transverse field

Bibliography

Landau, Huang, Kardar, Sethna, Peliti, Ma