Program Overview

Course Overview

The course SI2520, Nonequilibrium Statistical Mechanics, is a 7.5 credit course that introduces students to the common ideas and different approaches for studying systems in statistical mechanics that are not in equilibrium.

Course Description

Nonequilibrium situations are far more common in nature than equilibrium ones. This course gives an introduction to the common ideas and different approaches for studying systems in statistical mechanics that are not in equilibrium, i.e., with a time dependence in the description of the system. The course begins with a review of the origin of irreversibility and the second law of thermodynamics, which are at the foundations of equilibrium statistical mechanics. Various different techniques for studying non-equilibrium situations follow, which treat the problem on different levels of detail.

Course Contents

The main part of the course considers effective descriptions in terms of stochastic processes, closely related to simple random walk problems. The course also discusses:

• The Boltzmann equation, which provides a microscopic framework for studying transport in dilute systems, and leads up to coarse-grained hydrodynamic descriptions on longer length scales.
• The linear regime close to equilibrium, where it is possible to obtain the linear response of the system from its equilibrium fluctuations, via the fluctuation-dissipation theorem.
• Specific topics include:
  • Irreversibility and the second law of thermodynamics.
  • Brownian motion, random walks, the Langevin equation, the Fokker-Planck equation.
  • Stochastic processes in physics, master equations, one-step processes.
  • The Boltzmann equation, the H-theorem and irreversibility, conservation laws and hydrodynamics.
  • Open quantum systems and the Lindblad equation.
  • Quantum thermalization, quantum quenching, random matrix theory, the eigenstate thermalization hypothesis (ETH).

Intended Learning Outcomes

After the course, students shall:

• Have a broad overview of concepts, methods, and approaches within non-equilibrium statistical mechanics.
• Be able to model new physical situations using the methods exemplified in the course.
• Be able to generalize and apply the methods to new problems.
• Have gained insights into more advanced methods which touch upon modern research.

Literature and Preparations

• Specific prerequisites: English B / English 6.
• Recommended prerequisites: Introductory statistical physics and quantum mechanics.
• Literature: Information about course literature can be found in the course memo for the course offering or in the course room in Canvas.

Examination and Completion

• Grading scale: A, B, C, D, E, FX, F.
• Examination: TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F.
• Other requirements for final grade: The examination consists of written assignments, where the students' proposed written solutions are presented orally to the examiner.
• Examiner: Yunxiang Liao.

Ethical Approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further Information

• Course room in Canvas: Registered students find further information about the implementation of the course in the course room in Canvas.
• Offered by: SCI/Physics.
• Main field of study: Physics.
• Education cycle: Second cycle.
• Supplementary information: Reading course if there are few participants.