On the TASEP with second class particles

Eunghyun Lee

Research output: Contribution to journalArticle

Abstract

In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and N-1 second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at x and it is still the leftmost particle at time t. In particular, we show that this probability is expressed by the determinant of an N × N matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487-502].

Original languageEnglish
Article number006
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume14
DOIs
Publication statusPublished - Jan 12 2018

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Second Class Particle
Asymmetric Simple Exclusion Process
Initial conditions
Contour integral
Conditional probability
Determinant
Class

Keywords

  • Bethe ansatz
  • Second class particles
  • TASEP

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Cite this

On the TASEP with second class particles. / Lee, Eunghyun.

In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 14, 006, 12.01.2018.

Research output: Contribution to journalArticle

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