Lecture 6: Intro brownian motion

processes and Brownian motion problems

Introduction to the theory of stochastic processes and Brownian motion problems Lecture notes for a graduate course, These notes are an introduction to the theory of stochastic processes based on several sources. The presentation mainly follows the books of van Kampen [5] and Wio [6], except for the introduction , which is taken from the book of Gardiner [2] and the parts devoted to the Langevi...

Lecture 7: Brownian motion

Lecture 3: From Random Walks to Continuum Diffusion

In the previous lecture (by Prof. Yip), we discussed how individual particles undergo complicated, apparently random motion, in a liquid or gas, which is termed “diffusion”. The same erratic motion due to collisions can be observed at the macroscopic scale in the so­called Brownian motion of a dust particle in the air. A simulation of this phenomenon (java applet), shown in lecture, can be foun...

Non equilibrium statistical mechanics

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is devoted to a derivation of quantum master equations from the Schrödinger equation, and to some of their applications to quantum optics and to Brownian motion. Finally, in part III, I examine more recent d...

Random Walks and Brownian Motion

In today’s lecture we present the Brownian motion (BM). We start with an intuitive discussion, describing the BM as a limit of SRW. We present some of the BM properties and try to explain why we can expect these properties from a limit of SRW. We then give a formal definition for BM and prove such a process exists (Wiener 1923). Before the proof we give some important facts about the normal dis...