Statistical Physics
Prerequisiti
Course in Statistical Physics for third-year Physics students. Prerequisites:
Analytical Mechanics
Lagrangian and Hamiltonian formulations of mechanics, principles of least action, generalized coordinates, and conservation laws.
Classical Electrodynamics
Fundamental principles of electric and magnetic fields, Maxwell's equations, electromagnetic potentials, and gauge concepts.
Basic notions of thermodynamics
Heat and work, thermal machines, laws of Thermodynamics
Programma
- Laws of thermodynamics, thermodynamic potentials and Maxwell relations
- Kinetic theory of gases, Liouville equation, molecular chaos, Boltzmann equation and Maxwell-Boltzmann distribution
- Boltzmann H-theorem, arrow of time, notions of information theory, Shannon entropy, microcanonical ensemble
- Canonical ensemble, equipartition theorem of energy, grand canonical ensemble, equivalence of ensembles
- Interacting systems, cumulant expansion, cluster expansion, virial expansion, applications to real gases
- Van der Waals equation, Maxwell construction, introduction to first-order phase transitions
- Statistical theory of magnetism, Langevin diamagnetism and paramagnetism, Curie equation, Curie-Weiss model of ferromagnetism, one-dimensional Ising model
- Complements: introduction to non-equilibrium statistical physics, Brownian motion, Langevin equation, Jarzynski equality; introduction to the thermodynamics of information, Maxwell's paradox, Landauer's principle
- Quantum statistical physics: elementary notions, Bose gas and its properties, Fermi gas and its properties
- Theory of phase transitions: order parameters, Landau-Ginzburg theory, thermal fluctuations, critical exponents
Obiettivi formativi
Learn the key concepts of thermodynamics and statistical mechanics. Gain familiarity with the formalism of statistical mechanics and the theory of phase transitions.
Riferimenti bibliografici
Kerson Huang, Statistical Mechanics, second edition
Derek Frank Lawden, Principles of Thermodynamics and Statistical Mechanics
Luca Peliti, Statistical Mechanics in a Nutshell, second edition
Mehran Kardar, Statistical Physics of Particles