STATISTICAL PHYSICS I
Knowledge of basic thermodynamic notions, classical and quantum mechanics, elements of probability theory.
We remark that several quantum mechanical concepts, as density matrix, identical particles and Landau levels will be discussed in detail during the course.
The final examination consists of an oral interview, where the student is asked to describe in a quantitative way the proposed arguments, emphasizing the physically relevant results. In particular the student should have a clear idea of the physical nature of the problem, and which theoretical tools are to be applied to get quantitative predictions. In order to pass the exam the student has to present the physical nature of the problem in a correct perspective, and show at least a reasonable acquaintance with the analytic techniques that allow to get detailed predictions about the phenomenon. To get better grades the student has to exhibit more detailed mastering of the theoretical tools, and deeper physical insight of the subtler physical issues of the phenomenon. Top grade students should be able to attack in a correct way a new problem, slightly different from the cases discussed in the class.
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 gases. Since statistical mechanics provides a bridge between the microscopic description of a many particle system and its thermodynamic functions, this course might be of interest to many different curricula, from condensed matter, to astrophysics, to theoretical physics.
We expect that the student develops a quantitative understanding of the various techniques and relevant physical examples, discussed in the course, and she/he should be able to apply the formalism to novel physical settings.
Thermodynamics.
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 statistical mechanics.
Fundamentals of classical statistical mechanics, Gibbs ensembles. 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.
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.
The course consists of frontal lectures.
More detailed information can be obtained from my web page http://www.dfm.uninsubria.it/artuso/Roberto_web_page/Teaching.html, including a pdf copy and recordings of the lectures.
The students may contact me via email Roberto.artuso@uninsubria.it