Diffusion and Scattering of Shocks in the Partially Asymmetric Simple Exclusion Process
Vladimir Belitsky, Universidade de São Paulo
Gunter M. Schütz, Forschungszentrum Jülich
Abstract
We study the behavior of shocks in the asymmetric simple exclusion process
on Z whose initial distribution is a product measure with a finite number
of shocks. We prove
that if the particle hopping rates of this process are in a particular
relation with the densities of the initial measure then the distribution of
this process at any time is a linear combination of shock measures
of the structure similar to that of the initial distribution. The structure of
this linear combination allows us to interpret this result by saying that
the shocks of the initial distribution perform continuous time random walks
on Z interacting by the exclusion rule. We give explicit expressions
for the hopping rates of these random walks. The result is derived with a help
of quantum algebra technique. We made the presentation self-contained
for the benefit of readers not acquainted with this approach, but interested
in applying it in the study of interacting particle systems.
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