Advanced Statistical Physics: Non-Equilibrium Systems

This module introduces Brownian motion and explores three different derivations of this fundamental concept in statistical physics. Students will likely learn about the historical context, mathematical formulations, and physical interpretations of Brownian motion.

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This module focuses on continuous stochastic processes, extending the concepts from Brownian motion. Students will likely learn about the mathematical frameworks used to describe continuous random phenomena in physics and other fields.

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This module introduces stochastic differential equations, a key tool in modeling random dynamical systems. Students will likely learn about the formulation, interpretation, and solution methods for these equations in the context of statistical physics.

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This module covers the fluctuation dissipation theorem, a fundamental result in statistical physics. Students will likely learn about the relationship between fluctuations in a system at equilibrium and its response to external perturbations.

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This module introduces the Fokker Planck equation, a partial differential equation describing the time evolution of probability density functions. Students will likely learn about its derivation, applications, and relation to stochastic processes.

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This module covers Lévy flights, a type of random walk in which the step lengths have a probability distribution that is heavy-tailed. Students will likely learn about the properties, applications, and modeling of these processes in various physical systems.

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This module focuses on master equations, which describe the time evolution of a system probabilistically. Students will likely learn about their formulation, solution methods, and applications in statistical physics and other fields.

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This module introduces the Crook and Jarzynski equality, important results in non-equilibrium statistical mechanics. Students will likely learn about work fluctuations in non-equilibrium processes and their connection to equilibrium free energy differences.

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This two-part module introduces quantum optics and the quantum Langevin equation. Students will likely learn about the quantum description of light-matter interactions and the quantum analog of classical Langevin equations for open systems.

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This two-part module covers the quantum regression theorem, a powerful tool in quantum optics. Students will likely learn about its derivation, interpretation, and applications in calculating multi-time correlation functions of quantum systems.

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