The aim of the course is to provide an introduction to classical statistical mechanics in its traditional applications related to the thermodynamic properties of gases up to some more modern developments including phase transitions and critical phenomena.
Expected learning outcomes
The student at the end of the course will have acquired the following skills: 1) He/she will be able to perform elementary statistical and probabilistic operations. 2) He/she will know the relationship between Hamiltonian mechanics and thermodynamics. 3) He/she will be able to calculate the thermodynamic properties of a simple system from its Hamiltonian description. 4) He/she will know the properties of classical and quantum "ensembles" and will be able to determine to which cases to apply each ensemble. 5) He/she will have learned the different definitions of entropy. 6) He/she will know how to calculate the response of a system to an external perturbation. 7) He/she will know the properties of the Ising model in various dimensions. 8) He/she will know how to set an algorithm for the simulation of the Ising model. 9) He/she will be able to describe the properties of first and second order phase transitions.
Introduction to statistical mechanics Elements of probability theory Random walks Thermodynamic balance Phase space and ergodicity Entropy, disorder and information Canonical and Grand Canonical Ensemble Quantum statistical mechanics: Fermi and Bose distributions. Ising model Order parameters and symmetry breakage Correlations, response and dissipation First-rate phase transitions Nucleation and Coarsening Second order phase transitions Universality and scale invariance
Prerequisites for admission
To follow the course, it is necessary to know the basics of classical mechanics and thermodynamics, as taught in the first and second year of the three-year degree in physics.
The course includes a series of theoretical lessons and some exercises. The exercises include the solution of problems related to the program and some lessons in the computer room where students will have to simulate basic models of statistical physics (e.g. the Ising model). The theoretical lessons will be interspersed with short exercises proposed to the students in order to better consolidate the learning process.
James P. Sethna Statistical Mechanics: Entropy, Order Parameters and Complexity Oxford University Press
Assessment methods and Criteria
The exam will be written and will be divided into two parts: a part of exercises and some open-ended questions about the course program. The exercises in the computer room may include, but on an optional basis, the delivery of a simulation code.