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Statistical Physics II is a senior graduate/graduate course requiring the introductory course in statistical physics. The aim of the course is to give the student an introduction and an understanding of essential methods and points of view which together with a knowledge of the phenomena leads to an understanding of statistical physics. In the course of her/his studies the student will encounter examples in fundamental research where statistical physics plays an essential role. By working with theoretical models the student will learn how to construct and use physical models as a mean for the qualitative and quantitative explanation and understanding of various phenomena and processes. The student will work with texts and reflect on the content and argumentation with the purpose of putting statistical physics into perspective.
Review of equilibrium thermodynamics: first law and equilibrium, second law, variational statement of the second law, thermal equilibrium and temperature.
Review of the principles of statistical mechanics: the statistical methods and ensembles, microcanonical ensemble, canonical ensemble, generalised ensembles and Gibbs entropy formula. Alternative development of equilibrium distribution functions.
Non-interacting ideal systems: Photon gas, phonon gas, non-interacting fermions,
non-interacting bosons.
Phase transitions: Ising model, lattice gas, broken symmetry and range of correlations, Ising model in one dimension, mean field theory, Landau theory of phase transitions, critical exponents, scaling, renormalization group theory, Ising model in two dimensions.
Statistical mechanics of non-equilibrium systems: systems close to equilibrium, Onsager's regression hypothesis and time correlation functions, fluctuation-dissipation theorem, response function, Brownian motion, Langevin Equation, Fokker-Planck equation, master equation and detailed balance, systems far from equilibrium, the concepts of work and heat revisited, the fluctuation theorems, currents in non-equilibrium diffusive systems, out-of-equilibrium systems of biological interest, proteins under mechanical stress and molecular motors.
Numerical tools for statistical physics: the Monte Carlo algorithm.
After completion of the course the students are expected to be able to:
Alberto Imparato
6 hours per week divided in lectures, exercises, group work.
English
Introduction to Modern Statistical Mechanics by David Chandler and reading material provided by the teacher.
Exam: 2nd quarter
Re-exam: Arranged with lectu
Department of Physics and Astronomy
At the self-service https://mit.au.dk/
There will be an oral examination with the presence of an internal examiner. There is no preparation. The examination time will be circa 30 minutes. The student draws a question and gives a 10-15 minutes presentation. After that the examination has the form of a discussion.
