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.

Learning outcomes
1. Identify characteristic length and energy scales of a problem
2. Identify the correct technique to be used to tackle a particular problem
Knowledge
1. Connect microscopic description with macroscopic phenomena
2. Connect statistical description with quantum mechanics
Skills
1. Familiarity with the relation between statistical description and thermodynamics
2. Familiarity with the use of advanced mathematical techniques of statistical description
Competences
1. Perform exact analytical calculation using advanced mathematical techniques
2. Identify the limitations of an approximate methods and use them properly
3. 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.

Thermodynamic potentials
Gibbs Ensemble
Gibbs Ensemble in Quantum Mechanics
Real Gases and Liquid Theory
Fermi Ideal Gas
Bose Ideal Gas
Phase Transitions and Critical Phenomena
Atomistic origin of Magnetism, Ising and Heisenberg models
Ising Model, exact solutions and mean field theories
Boltzmann equation and H-Theorem

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)

Assessment methods
Written and oral exams

Detailed description of the assessment methods
Detailed description of the assessment methods. Written and oral exam.
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. Those students that will be unable to pass the homework, will be given the possibility of taking an in class closed book written exam in each exam session. A successful outcome in this written exam will allow them to take the oral exam. Both homeworks and written exams are valid until the end of December of the year successive the end of the semester.
The oral exam will last approximately 40 minutes with two questions on the topics discussed in class. Grading will be as follows. Solid knowledge of the requested topics (20 points); Clarity in the exposition (5 points); Confidence in the knowledge (5 points).

Teaching methods
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

Care will be exercised to make sure that the present course is coherent with the course of Physics of Complex Systems that can be reckoned as the continuation of the present course, including many modern applications of the formalism of Statistical Mechanics

written and oral