Equivalent T-Q relations and exact results for the open TASEP

Nicolas Crampe, Rafael Nepomechie

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Starting from the Bethe ansatz solution for the open totally asymmetric simple exclusion process (TASEP), we compute the largest eigenvalue of the deformed Markovian matrix, in exact agreement with results obtained by the matrix ansatz. We also compute the eigenvalues of the higher conserved charges. The key step is to find a simpler equivalent T-Q relation, which is similar to the one for the TASEP with periodic boundary conditions.

Original languageEnglish (US)
Article number103105
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2018
Issue number10
DOIs
StatePublished - Oct 24 2018

Fingerprint

Asymmetric Simple Exclusion Process
Exact Results
exclusion
eigenvalues
Bethe Ansatz
Largest Eigenvalue
matrices
Periodic Boundary Conditions
Charge
boundary conditions
Eigenvalue
Exclusion
Eigenvalues
Boundary conditions

Keywords

  • exact results
  • exclusion processes
  • integrable spin chains and vertex models
  • quantum integrability (Bethe ansatz)

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Equivalent T-Q relations and exact results for the open TASEP. / Crampe, Nicolas; Nepomechie, Rafael.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, No. 10, 103105, 24.10.2018.

Research output: Contribution to journalArticle

@article{a724b4b95e60438ea02451f285fd8f57,
title = "Equivalent T-Q relations and exact results for the open TASEP",
abstract = "Starting from the Bethe ansatz solution for the open totally asymmetric simple exclusion process (TASEP), we compute the largest eigenvalue of the deformed Markovian matrix, in exact agreement with results obtained by the matrix ansatz. We also compute the eigenvalues of the higher conserved charges. The key step is to find a simpler equivalent T-Q relation, which is similar to the one for the TASEP with periodic boundary conditions.",
keywords = "exact results, exclusion processes, integrable spin chains and vertex models, quantum integrability (Bethe ansatz)",
author = "Nicolas Crampe and Rafael Nepomechie",
year = "2018",
month = "10",
day = "24",
doi = "10.1088/1742-5468/aae2e0",
language = "English (US)",
volume = "2018",
journal = "Journal of Statistical Mechanics: Theory and Experiment",
issn = "1742-5468",
publisher = "IOP Publishing Ltd.",
number = "10",

}

TY - JOUR

T1 - Equivalent T-Q relations and exact results for the open TASEP

AU - Crampe, Nicolas

AU - Nepomechie, Rafael

PY - 2018/10/24

Y1 - 2018/10/24

N2 - Starting from the Bethe ansatz solution for the open totally asymmetric simple exclusion process (TASEP), we compute the largest eigenvalue of the deformed Markovian matrix, in exact agreement with results obtained by the matrix ansatz. We also compute the eigenvalues of the higher conserved charges. The key step is to find a simpler equivalent T-Q relation, which is similar to the one for the TASEP with periodic boundary conditions.

AB - Starting from the Bethe ansatz solution for the open totally asymmetric simple exclusion process (TASEP), we compute the largest eigenvalue of the deformed Markovian matrix, in exact agreement with results obtained by the matrix ansatz. We also compute the eigenvalues of the higher conserved charges. The key step is to find a simpler equivalent T-Q relation, which is similar to the one for the TASEP with periodic boundary conditions.

KW - exact results

KW - exclusion processes

KW - integrable spin chains and vertex models

KW - quantum integrability (Bethe ansatz)

UR - http://www.scopus.com/inward/record.url?scp=85056092711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056092711&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/aae2e0

DO - 10.1088/1742-5468/aae2e0

M3 - Article

AN - SCOPUS:85056092711

VL - 2018

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 10

M1 - 103105

ER -