Current Fluctuations in the Asymmetric Simple Exclusion Process and Bethe Ansatz - Part II
- Event time: 2:00pm
- Event date: 30th September 2008
- Speaker: Sylvain Prolhac (University of Edinburgh)
- Location: Room 3315, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
In this second part, after recalling briefly how the Bethe Ansatz is used for the calculation of the current fluctuations in the asymmetric simple exclusion process on a ring, I will show that the Bethe equations can be conveniently rewritten as a functional equation. This functional equation can be solved exactly in the totally asymmetric case, giving access to the complete fluctuations of the current. For the general case of a partial asymmetry, a complete solution is not known: only the three first cumulants of the current have been calculated. I will discuss the two interesting scaling limits for which these cumulants take simple expressions. These two scaling limits can be understood by simple physical arguments.
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..