Introduction to Stochastic Processes: Comparison between Non-interacting and Interacting Systems

Condensed Matter lunchtime seminar

Introduction to Stochastic Processes: Comparison between Non-interacting and Interacting Systems

  • Event time: 1:00pm
  • Event date: 6th November 2000
  • Speaker: Isao Hiyane (University of Edinburgh)
  • Location: Room 2511,

Event details

In this introductory seminar, the one-dimensional systems in which each particle can hop to the right nearest neighbour site only are presented. If the particles do not interact with each other, each particle can be treated independently, reducing the problem to one body. In this non-interacting system, the particles obey the Poisson process [1], which is exactly solvable. However, once one restricts the particles so that each site can have at most one particle, that is, a particle can not hop to the site which is occupied by another particle, then the story is drastically different. Due to the hard-core exclusion, the particles can no longer be treated independently, but they obey the totally asymmetric simple exclusion process (TASEP) [2], which is a current research topic. The density profile and current of the above two systems are discussed. Undergraduates who are interested in studying Statistical Mechanics further are also welcome.
[1] N.G. van Kampen, Stochastic Processes in Physics and Chemistry North-Holland, (1992)
[2] B. Derrida, M.R. Evans, V. Hakim and V. Pasquier, J. Phys. A 26, 1493 (1993)

This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..

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