Instability transitions and ensemble equivalence in diffusive flow

by Dr Meesoon Ha (KAIST)

Wednesday 28 May 2008, 13:00 → 14:00 Europe/Stockholm

Nordita seminar room

The role of boundary and bias are tested in one-dimensional stochastic flow with competing nonlocal and local hopping events, where we use the totally asymmetric simple exclusion process (TASEP) and the symmetric simple exclusion process (SSEP), respectively. With open boundaries, both systems undergo dynamic instability transitions from a populated finite density phase to an empty road (ER) phase as the nonlocal hopping rate increases. Nonlocal skids in principle promote strong clustering, but such clusters are stable only at the transition for the unbiased case, while they are stable in the whole populated phase for the biased case. Using such a cluster stability analysis, we determine the location of nonequilibrium phase transitions, their nature, and scaling properties, which agrees well with numerical results. Our cluster analysis provides a physical insight into the mechanism behind such transitions. For the biased case with open boundaries, we numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk controls is in control. For the unbiased case with open boundaries, the transition is always abrupt, i.e., first order as long as there is the left-right symmetry. The first-order transition originates from a turnabout of the cluster drift velocity for the biased case where the current remain analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise at the critical line, while such an abrupt transition is attributed to the cluster stability for the unbiased case, which is in contrast to the same unbiased case with periodic boundary conditions where the continuous one has been observed. Finally, we discuss the equivalence of ensembles in the generalized TASEP as well as the generalized SSEP with the thermodynamic limiting states.