31552 - Statistical Mechanics 1

Learning outcomes

At the end of the course, the student knows the statistical laws that rule the thermodynamic behavior of macroscopic systems with a high number of particles and is able to describe the principal applications to both classical and quantum gases and to magnetic systems.

Course contents

We will study the theoretical bases of classical and quantum statistical mechanics. Special attention will be paid to the study of paradigmatic models and of applications to relevant systems in physics.

Foundations of Classical Statistical Mechanics

- Review of thermodynamics and mechanics.

- The microscopic interpretation of thermodynamics: microcanonical, canonical and grandcanonical ensembles; partition functions and thermodynamic quantities.

- Probabilistic interpretation and counting of states; entropy.

- Examples and applications such as: ideal gas; van der Waals gas; gas of harmonic oscillators; classical magnetism.

Foundations of Quantum Statistical Mechanics

- Review of quantum mechanics: density matrices, pure and mixed states.

- Identical particles: bosons and fermions. The formalism of second quantization for the description of many body systems.

- Microcanonical, canonical and grandcanonical ensembles; partition functions, entropy and other thermodynamic quantities.

- Freequantum gases; non-relativistic boson gas and Bose-Einstein condensation; fermionic gas and degeneration limit; specific heats.

- Examples and applications such as: quantum gases; photon gas, ultra relativistic sermonic gas, Landau Magnetism, phonons.

 

Readings/Bibliography

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

[2] R.K. Pathria, Statistical Mechanics, Butterworth.

[3] K. Huang, Meccanica Statistica, Zanichelli (available also in English) 

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 analysed in class.

Teaching tools

Text and solution of complements/exercises analysed in class are available in AlmaDL.

Office hours

See the website of Elisa Ercolessi