Langevin dynamics: Path Integral Methods

This lecture covers Langevin dynamics, a model of Brownian motion combining viscous drag and random collisions, along with the Fokker-Planck equation and its correspondence with stochastic differential equations. It also discusses solving the Langevin equation, the stationary solution, and finite-time propagation. Additionally, it explores Langevin dynamics as a thermostat in a molecular dynamics framework, emphasizing the simplification provided by the free-particle propagator. The efficiency of Langevin sampling is highlighted, showing how harmonic Langevin dynamics can be solved analytically. The take-home message stresses the use of Langevin dynamics for sampling the canonical ensemble and the importance of critical damping for optimal sampling efficiency.