Current Fluctuations in the exclusion process and Bethe Ansatz

Abstract

We use the Bethe Ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps. The Bethe equations are highly coupled and this fact has impeded their use to derive exact results for finite systems. We overcome this technical difficulty by a reformulation of the Bethe equations into a one variable polynomial problem, akin to the functional Bethe Ansatz. The perturbative solution of this equation leads to the cumulants of the current. We calculate here the first two orders and derive exact formulae for the mean value of the current and its fluctuations.

17 pages

References in corpus (6)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Traffic of molecular motors through tube-like compartments
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Full counting statistics of nano-electromechanical systems
• Current noise in a vibrating quantum dot array
• Bethe ansatz solution of zero-range process with nonuniform stationary state

Cited by in corpus (5)

• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Cumulants of the current in the weakly asymmetric exclusion process
• Fluctuations and skewness of the current in the partially asymmetric exclusion process