Asymmetric exclusion model with several kinds of impurities

Abstract

We formulate a new integrable asymmetric exclusion process with $N-1=0,1,2,...$ kinds of impurities and with hierarchically ordered dynamics. The model we proposed displays the full spectrum of the simple asymmetric exclusion model plus new levels. The first excited state belongs to these new levels and displays unusual scaling exponents. We conjecture that, while the simple asymmetric exclusion process without impurities belongs to the KPZ universality class with dynamical exponent 3/2, our model has a scaling exponent $3/2+N-1$. In order to check the conjecture, we solve numerically the Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found the dynamical exponents 7/2 and 9/2 in these cases.

to appear in JSTAT

References in corpus (10)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Spectral gap of the totally asymmetric exclusion process at arbitrary filling
• Exact solutions of exactly integrable quantum chains by a matrix product ansatz
• The Bethe ansatz as a matrix product ansatz
• Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
• Generalization of the matrix product ansatz for integrable chains
• The Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz
• Asymmetric exclusion model with impurities
• The Matrix Product Ansatz for integrable U(1)^N models in Lunin-Maldacena backgrounds

Cited by in corpus (1)

• Asymmetric exclusion processes on a closed network with bottlenecks