31921 - Statistical Mechanics 2

Learning outcomes

At the end of the course, the student knows the mathematical concepts at the foundation of statistical mechanics and is able to study analytically a large class of interacting models, including their critical phenomena.

Course contents

We will study the theoretical foundations of classical and quantum statistical mechanics also for non-equilibrium systems.

Interacting systems and approximation techniques

- Theory of phase transitions, spontaneous symmetry breaking

- Hartree-Fock approximation: variational technique and applications to particle gases

- Superfluidity: phenomenology, microscopic theory

- Superconductivity: phenomenology, microscopic theory and Ginzburg-Landau approach

- Ginzburg Landau Theory for the O(N) model: order parameter, correlations and critical exponents

Correlations and Fluctuations

- Time-dependent Observables and Correlations in the classical and quantum case

- Linear response theory; the Fluctuation-Dissipation theorem

- Introduction to stochastic dynamics: Brownian motion

- Stochastic processes: Master Equation, Fokker-Plank equation, Markov chains, applications

Readings/Bibliography

[1] G. Morandi, F. Napoli, E Ercolessi, Statistical Mechanics, World Scientific. 

[2] R.K. Pathria, P.D. Beale, Statistical Mechanics, Elsevier.

[3] L.E. Reichl, A Modern Course in Statistical Physics, Wiley.

[4] J. F. Annett, Superconductivity, Superfluids and Condensates, Oxford.

[5] L.H. Ryder, Quantum Field Theory, Cambridge 

Teaching methods

Theoretical topics are fully explained in class by the teacher.  
Some classes will be devoted to exercises that students will solve under the teacher's supervision.

Assessment methods

Oral exam.  
Questions will cover both the theoretical part and the exercises treated in class.

Teaching tools

Text and solution of applications and exercises studied in class.

Office hours

See the website of Elisa Ercolessi