On the blockage problem and the non-analyticity of the current for the parallel TASEP on a ring

Abstract

The Totally Asymmetric Simple Exclusion Process (TASEP) is an important example of a particle system driven by an irreversible Markov chain. In this paper we give a simple yet rigorous derivation of the chain stationary measure in the case of parallel updating rule. In this parallel framework we then consider the blockage problem (aka slow bond problem). We find the exact expression of the current for an arbitrary blockage intensity ε in the case of the so-called rule-184 cellular automaton, i.e. a parallel TASEP where at each step all particles free-to-move are actually moved. Finally, we investigate through numerical experiments the conjecture that for parallel updates other than rule-184 the current may be non-analytic in the blockage intensity around the value ε = 0.

Defect-induced phase transition in the asymmetric simple exclusion process

“…Recently the problem has been newly addressed in the mathematical literature, in a series of works [8][9][10][11]. In [8], based on analytical arguments from series expansions and results for related systems (e.g.…”

“…Recently the problem has been newly addressed in the mathematical literature, in a series of works [8][9][10][11]. In [8], based on analytical arguments from series expansions and results for related systems (e.g., directed polymers) it was argued that an arbitrarily small defect in a TASEP with open boundaries will have global effects, e.g.…”