# Asymmetric simple exclusion process on a ring conditioned on enhanced flux

Abstract : We show that in the asymmetric simple exclusion process (ASEP) on a ring, conditioned on carrying a large flux, the particle experience an effective long-range potential which in the limit of very large flux takes the simple form $U= -2\sum_{i\neq j}\log|\sin\pi(n_{i}/L-n_{j}/L)|$, where $n_{1}% n_{2},\ldots n_{N}$ are the particle positions, similar to the effective potential between the eigenvalues of the circular unitary ensemble in random matrices. Effective hopping rates and various quasistationary probabilities under such a conditioning are found analytically using the Bethe ansatz and determinantal free fermion techniques. Our asymptotic results extend to the limit of large current and large activity for a family of reaction-diffusion processes with on-site exclusion between particles. We point out an intriguing generic relation between classical stationary probability distributions for conditioned dynamics and quantum ground state wave functions, in particular, in the case of exclusion processes, for free fermions.
Type de document :
Pré-publication, Document de travail
submitted to J. Stat. Mech. 2010

https://hal.archives-ouvertes.fr/hal-00536337
Contributeur : Damien Simon <>
Soumis le : mardi 16 novembre 2010 - 07:10:06
Dernière modification le : mercredi 21 mars 2018 - 18:56:48

### Identifiants

• HAL Id : hal-00536337, version 1
• ARXIV : 1007.4892

### Citation

Vladislav Popkov, Gunter M. Schütz, Damien Simon. Asymmetric simple exclusion process on a ring conditioned on enhanced flux. submitted to J. Stat. Mech. 2010. 〈hal-00536337〉

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