STATISTICAL MECHANICS

This course is offered during the first semester of the first year and is a core (i.e. required) course for all first year students. It relies on the knowledge of a scientific first degree to set up a rigorous theory of complex systems at the microscopic level. Starting from a brief reminder of basic thermodynamics, the course will introduce the formalism of Statistical Mechanics for both classical and quantum systems, as well as classical and quantum statistics. Selected applications will be illustrated both in class and as homework exercises to be solved by the students, to display the power of this formalism in different fields. Non-equilibrium phenomena and transport properties will also be discussed.

Upon exiting from this course, students will be able to
1. Identify characteristic length and energy scales of a problem
2. Connect microscopic description with macroscopic phenomena
3. Perform exact analytical calculation using advanced mathematical techniques
4. Identify the limitations of an approximate methods and use them properly
5. Read any advanced paper/book on this topic on their own

Knowledge of all mathematical tools at the level of those offered by the course of Mathematical Methods of Physics or similar, is required. Also required is the knowledge of classical physics (Classical Mechanics, Thermodynamics, Electromagnetism) as covered in conventional scientific first degree programs and a previous exposition to the principle of quantum mechanics at the level of that covered by an introductory course of quantum mechanics.

The Laws of Thermodynamics.
Some Applications of Thermodynamics.
The Problem of Kinetic Theory.
The Equilibrium State of a Dilute Gas.
Transport Phenomena.
Classical Statistical Mechanics.
Canonical Ensemble and Grand Canonical Ensemble.
Quantum Statistical Mechanics.
General Properties of the Partition Function.
Approximate Methods.
Fermi Systems.
Bose Systems.
Superfluids.
Ising Model.
Critical Phenomena.
The Landau Approach.
Renormalization Group

Mehran Kardar, Statistical Physics of Particles Cambridge University press (2007).
Mehran Kardar, Statistical Physics of Fields Cambridge University press (2007).
P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge university Press (1995)
Kerson Huang, Statistical Mechanics John Wiley&Sons (1987)
F. Reif: Fundamental of Statistical and Thermal Physics (MC Graw Hill 1987)
C. Kittel e H. Kroemer: Termodinamica Statistica (Boringhieri 1985)
L. Reichl: A Modern Course in Statistical Physics (University of Texas 1980)
H. B. Callen: Thermodynamics and an Introduction to Thermostatics (Wiley & Son 1985)

Final grade will be the average of an oral exam (worth 50% of the final grade) and of the average grade reported on homeworks that will be assigned during the semester (and worth the additional 50% of the final grade). All homeworks must be handed in within the due date. Failure to do that will result into the impossibility of taking the oral exam. Later turning in will be penalized in terms of grades. The allotted time for each homework will be on average three weeks.

All calculations will be spelled out in details on a digital blackboard, use will be made of selected more complex examples requiring numerical solutions. These will provide the student with an additional expertise in numerical calculations.
Lecture recording as well as supporting materials will also be available at the instructor moodle learning platform.

English

written and oral