A simple symmetric exclusion process driven by an asymmetric tracer particle
| When |
Mar 13, 2020
from 10:15 to 11:15 |
|---|---|
| Where | salle 435 |
| Attendees |
Arvind Ayyer (Indian Institute of Science, Bangalore) |
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We consider an exclusion process on a periodic one-dimensional lattice
where all particles perform simple symmetric exclusion except for a
`tracer particle', which performs partially asymmetric exclusion with
forward and backward rates p and q respectively. This process and its
variants have been investigated starting with Ferrari, Goldstein and
Lebowitz (1985) to understand the validity of the Einstein relation. We
proveproduct formulas for stationary weights and exact formulas for the
nonequilibrium partition function in terms of combinatorics of set
partitions. We will also compute the current, and the density profile as
seen by the test particle. We will then perform asymptotics to
understand the thermodynamic limit.One perhaps surprising feature of
this process is that the nonequilibrium free energy is not well-defined
for this system in the thermodynamic limit. This talk is based on the
preprint arXiv:2001.02425.