A simple symmetric exclusion process driven by an asymmetric tracer particle

par Arvind Ayyer (Indian Institute of Science, Bangalore)

vendredi 13 mars 2020, 10:15 → 11:15 Europe/Paris

Salle 435 (ENS de Lyon, site Monod)

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.