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An exact solution for a simple reaction-diffusion lattice modelMathematical Physics & Probability
|Speaker: ||Arvind Ayyer, Institut de Physique Theorique CEA Saclay|
|Location: ||1147 MSB|
|Start time: ||Wed, Jun 2 2010, 4:10PM|
Inspired by the border process of Glauber dynamics in the one dimensional
Ising model, we consider a nonequilibrium exclusion process on a finite
open lattice with both hopping and annihilation rates. The process is
defined as a Markov chain. We obtain the steady state distribution of the
chain exactly for any finite size using a new approach that we call the
"transfer matrix ansatz". We also calculate physical quantities such as
the "partition function", densities and two-point functions in this model.
Lastly, we had an explicit conjecture for all the eigenvalues of the
corresponding transition matrix, which was proven subsequently by Volker
Strehl. This is joint work with Kirone Mallick.