Main aim of this course is providing, by means of statistical and probabilistic methods, a rationale for the thermodynamic description and a bottom-up description of the structural and dynamic properties of materials. These concepts are then applied to the description of systems of specific interest in engineering applications, such as liquids, plasmas, disordered solids (glasses and gels) and magnetic materials, and to investigate physical problems of technological relevance such as phase transitions, superfluidity and superconductivity.

At the end of the course, students should

• Know and master the fundamental ideas of statistical physics and the basic tools, such as statistical ensembles and partition functions, which allow to relate the microscopic world to the macroscopic realm of thermodynamics;
• Manage to apply the former general concepts to topics in condensed matter and material science of interest for their specific course of studies.  
• Be capable of conveying the knowledge they have acquired with plainness but also with accuracy and the ability to synthetize the argument (even for an audience that may not be as learned in the field as their teacher).  

1. Review of probability and statistics. Probability distributions of interest in physics. Statistical entropy. Brownian motion as a paradigm of stochastic processes in physics.

2. From the macroworld to the microworld. Review of thermodynamics. Physical description of classical and quantum many-particle systems. Phase space and Liouville theorem. Density of quantum microstates and its dependence on total energy.

3. Foundations of statistical mechanics. Boltzmann fundamental postulate. Microcanonical distribution and thermodynamics. Gibbs paradox and Maxwell-Boltzmann (MB) approximation.

4. Closed systems and canonical distribution. Partition function and free Energy. Average value and fluctuations of internal variables. Canonical distribution for independent particles and system of indistinguishable particles. Classical monatomic gas. Polyatomic gases. Einstein and Debye models for the specific heat of solids. Phonons in solids. Paramagnetism and diamagnetism. Bohr-van Leewen theorem.

5. Mean field theories. Van der Waals model of the liquid-gas transition. Ferromagnetism and Curie-Weiss theory. Plasmas in the Debye-Hückel approximation.

6. Open systems and gran-canonical distribution. Chemical potential. Langmuir adsorption isotherm. Inhomogeneous systems and local chemical potential. Colloidal dispersions. Quantum statistics. Weakly-degenerate gases. Fermi gas and Sommerfeld theory for electrons in metals. Degenerate Bose gas and Bose-Einstein (BE) condensation. Laser cooling and BE condensation in dilute gases confined by magneto-optical traps.

7. Highly correlated systems. Liquid structure. Density correlations and structure factor. Superfluidity in ⁴He and Landau-Tisza phenomenological model. Superconductivity (hints).

To attend the course a solid knowledge of basic physics and a good mastering of calculus are required. To fully appreciate all the subjects presented in the course, some elementary notions of probability, quantum mechanics, and atomic physics may also be particularly useful, although not strictly necessary since short reviews of their basic concepts will preliminarily be provided by the teacher when needed (see for instance Topics 1 and 2 above).

The evaluation consists in an oral examination, structured so to ascertain whether and to what extent the goals of the course have been reached. Specifically, the student is first asked to give a concise introduction to one of the general subjects discussed in the course, so to check her/his skills in summarizing and framing an argument. Practical mastering of the acquired knowledge is then verified by asking the student to explicitly derive some of the main results related to that topic (namely, the student should be able to combine synthetic with analytic skills), focusing on a specific application of the discussed subject to the main subject of his/her studies. For the overall evaluation, a yardstick of the student’s performance, besides the clarity and effectiveness of the exposition, will also be the skill in using an appropriate scientific language and the readiness in finding connections between different topics. The final assessment will also take into account the degree of incremental knowledge acquired by student with respect to her/his starting level.

A good introduction to Statistical Physics

A "classic" and still very valid textbook of Statistical Mechanics

A very good textbook concerning the applications of statistical methods to condensed matter physics