Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) on a periodic one-dimensional lattice of L sites. Using Bethe ansatz, we derive parametric formulas for the eigenvalues of its generator in the thermodynamic limit. This allows to study the curve delimiting the edge of the spectrum in the complex plane. A functional integration over the eigenstates leads to an expression for the density of eigenvalues in the bulk of the spectrum. The density vanishes with an exponent 2/5 close to the eigenvalue 0.

40 pages

References in corpus (10)

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Cited by in corpus (10)

• Bethe Ansatz and Q-operator for the open ASEP
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Solution of the Kolmogorov equation for TASEP
• KPZ fluctuations in finite volume
• Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
• Fluctuations of TASEP on a ring in relaxation time scale