Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution

Abstract

The probability distribution of the current in the asymmetric simple exclusion process is expected to undergo a phase transition in the regime of weak asymmetry of the jumping rates. This transition was first predicted by Bodineau and Derrida using a linear stability analysis of the hydrodynamical limit of the process and further arguments have been given by Mallick and Prolhac. However it has been impossible so far to study what happens after the transition. The present paper presents an analysis of the large deviation function of the current on both sides of the transition from a Bethe ansatz approach of the weak asymmetry regime of the exclusion process.

accepted to J.Stat.Phys, 1 figure, 1 reference, 2 paragraphs added

References in corpus (6)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• A numerical approach to large deviations in continuous-time
• Cumulants and large deviations of the current through non-equilibrium steady states
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries

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