13 research outputs found
Relaxation rate of the reverse biased asymmetric exclusion process
We compute the exact relaxation rate of the partially asymmetric exclusion
process with open boundaries, with boundary rates opposing the preferred
direction of flow in the bulk. This reverse bias introduces a length scale in
the system, at which we find a crossover between exponential and algebraic
relaxation on the coexistence line. Our results follow from a careful analysis
of the Bethe ansatz root structure.Comment: 22 pages, 12 figure
Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
We revisit the totally asymmetric simple exclusion process with open
boundaries (TASEP), focussing on the recent discovery by de Gier and Essler
that the model has a dynamical transition along a nontrivial line in the phase
diagram. This line coincides neither with any change in the steady-state
properties of the TASEP, nor the corresponding line predicted by domain wall
theory. We provide numerical evidence that the TASEP indeed has a dynamical
transition along the de Gier-Essler line, finding that the most convincing
evidence was obtained from Density Matrix Renormalisation Group (DMRG)
calculations. By contrast, we find that the dynamical transition is rather hard
to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss
in general terms scenarios that admit a distinction between static and dynamic
phase behaviour.Comment: 27 pages, 18 figures. v2 to appear in J Phys A features minor
corrections and better-quality figure
Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
Unlike equilibrium statistical mechanics, with its well-established
foundations, a similar widely-accepted framework for non-equilibrium
statistical mechanics (NESM) remains elusive. Here, we review some of the many
recent activities on NESM, focusing on some of the fundamental issues and
general aspects. Using the language of stochastic Markov processes, we
emphasize general properties of the evolution of configurational probabilities,
as described by master equations. Of particular interest are systems in which
the dynamics violate detailed balance, since such systems serve to model a wide
variety of phenomena in nature. We next review two distinct approaches for
investigating such problems. One approach focuses on models sufficiently simple
to allow us to find exact, analytic, non-trivial results. We provide detailed
mathematical analyses of a one-dimensional continuous-time lattice gas, the
totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic
model for NESM, much like the role the Ising model played for equilibrium
statistical mechanics. It is also the starting point for the second approach,
which attempts to include more realistic ingredients in order to be more
applicable to systems in nature. Restricting ourselves to the area of
biophysics and cellular biology, we review a number of models that are relevant
for transport phenomena. Successes and limitations of these simple models are
also highlighted.Comment: 72 pages, 18 figures, Accepted to: Reports on Progress in Physic