Introduction to the theory of stochastic processes and Brownian motion problems
by J. L. Garcia-Palacios
Publisher: arXiv 2007
Number of pages: 104
Contents: Historical introduction; Stochastic variables; Stochastic processes and Markov processes; The master equation: Kramers–Moyal expansion and Fokker–Planck equation; The Langevin equation; Linear response theory, dynamical susceptibilities, and relaxation times (Kramers’ theory); Methods for solving Langevin and Fokker–Planck equations; Derivation of Langevin equations in the bath-of-oscillators formalism.
Home page url
Download or read it online for free here:
by Gunnar Pruessner - Imperial College London
This is an attempt to deliver, within a couple of hours, a few key-concepts of non-equilibrium statistical mechanics. The goal is to develop some ideas of contemporary research. Many of the ideas are illustrated or even introduced by examples.
by R. J. Baxter - Academic Press
This text explores the solution of two-dimensional lattice models. Topics include basic statistical mechanics, Ising models, mean field model, spherical model, ice-type models, corner transfer matrices, hard hexagonal models, and elliptic functions.
by E. Ben-Naim, P. L. Krapivsky, S. Redner - Boston University
The authors discuss the development of basic kinetic approaches to more complex and contemporary systems. Among the large menu of stochastic and irreversible processes, we chose the ones that we consider to be among the most instructive.
by Oleg Kupervasser - arXiv
Statistical classical mechanics and quantum mechanics are two developed theories that contain a number of paradoxes. However the given paradoxes can be resolved within the framework of the existing physics, without introduction of new laws.