Degree course: 
Corso di Second cycle degree in PHYSICS
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Compulsory subjects, characteristic of the class
First Semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (48 hours)

Knowledge of basic thermodynamic notions, classical and quantum mechanics, elements of probability theory.

Final Examination: 

The final examination consists of an oral interview, where the student is asked to describe in a quantitative way the proposed arguments, emphasising the physically relevant results.

Voto Finale

The goal is to provide a detailed knowledge of the principles of statistical mechanics of quantum and classical balance, describe approximation methods, and provide a detailed description of the main phenomena related to perfect quantum gas. We expect that the student ripen quantitative understanding and be able to deal with exercises and insights in this area.

Thermodynamics. [10h]
Equilibrium states, thermodynamics, state functions, zeroth law. First principle. Equation of state of a perfect gas. Response functions. Second principle (Clausius), Carnot's theorem and entropy. Relationship between response functions. Stability of equilibrium states, thermodynamic potentials and their convexity properties. Maxwell's relations. The third law. Thermodynamic description of phase transitions. The coexistence curve and Clausius Clapeyron equation. Van der Waals equation of state, critical point and the law of corresponding States. Maxwell construction. Critical exponents and their value for the case of Van der Waals. Landau theories, evaluation of critical exponents.
Fundamentals of statiscical mechanics. [22h]
Fundamentals of classical statistical mechanics, Gibbs ensemples. Microcanonical ensemble formalism. The ideal gas. Gibbs paradox and the Boltzmann factor. Equipartition theorem. The canonical formulation. Equivalence of ensembles. Model for the Van der Waals equation. Grand canonical ensemble and equivalence with the canonical ensemble. Langmuir adsorption isotherm. Existence of the thermodynamic limit for Van Hove potentials. Cluster and virial expansions. Second virial coefficient for simple potentials. Density matrices in quantum mechanics, identical particles systems, quantum Gibbs ensembles. Classical limit of quantum partition function.
Perfect quantum gases. [16h]
Bose gases: crystal lattice in Debye approximation, specific heat at low and high temperatures. Bose-Einstein condensation: the population of the state of minimum energy, interpretation as first order phase transition. Degenerate Fermi Gas, Fermi energy and chemical potential, specific heat at low temperatures. Pauli paramagnetism and Landau diamagnetism.

Thermodynamic description. First and second principle.
Stability of equilibrium states. Thermodynamic potentials.
Third law. Clausius Clapeyron equation.
Van der Waals equation of state.
Landau theories.
Foundations of statistical mechanics
The microcanonical ensemble
The canonical ensemble. Tonks-Van der Waals gas.
The grand canonical ensemble.
The thermodynamic limit (Van Hove gas)
The thermodynamic limit (lattice models). Cluster expansion.
The second virial coefficient.
Quantum statistical mechanics.
Grand canonical partition function for bosons.
Grand canonical partition function for fermions.
The classical limit of the quantum partition function.
Bose statistics: phonons.
Debye theory.
Bose Einstein condensation.
Degenerate Fermi gas.
Pauli paramagnetism. Landau diamagnetism.

K. Huang, Statistical Mechanics; M. Kardar, Statistical Physics of Particles ; L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1; L.E. Reichl, A Modern Course in Statistical Physics .

The course consists of frontal lectures.

More detailed informations can be obtained from my web page, including a pdf copy and recordings of the lectures.