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Contributed Seminar: Exact solution of the dynamics of the PASEP with open boundaries

Presented by: 
J de Gier [Melbourne]
Date: 
Friday 31st March 2006 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
Abstract: 

The dynamics of the asymmetric exclusion process is governed by the spectrum of its transition matrix. In particular its lowest excited state describes the approach to stationarity at large times. I will discuss the exact diagonalisation of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. The resulting Bethe ansatz equations describe the {\em complete} spectrum of the transition matrix. For totally asymmetric diffusion I will present exact results for the spectral gap and derive the dynamical phase diagram. We observe boundary induced crossovers in and between massive, diffusive and KPZ scaling regimes.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons