{"title":"Integrability of the Multi-Species Asymmetric Simple Exclusion Processes with Long-Range Jumps on ℤ","authors":"Eunghyun Lee","doi":"10.3390/sym16091164","DOIUrl":null,"url":null,"abstract":"Let us consider a two-sided multi-species stochastic particle model with finitely many particles on Z, defined as follows. Suppose that each particle is labelled by a positive integer l, and waits a random time exponentially distributed with rate 1. It then chooses the right direction to jump with probability p, or the left direction with probability q=1−p. If the particle chooses the right direction, it jumps to the nearest site occupied by a particle l′<l (with the convention that an empty site is considered as a particle with labelled 0). If the particle chooses the left direction, it jumps to the next site on the left only if that site is either empty or occupied by a particle l′<l, and in the latter case, particles l and l′ swap their positions. We show that this model is integrable, and provide the exact formula of the transition probability using the Bethe ansatz.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"37 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym16091164","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let us consider a two-sided multi-species stochastic particle model with finitely many particles on Z, defined as follows. Suppose that each particle is labelled by a positive integer l, and waits a random time exponentially distributed with rate 1. It then chooses the right direction to jump with probability p, or the left direction with probability q=1−p. If the particle chooses the right direction, it jumps to the nearest site occupied by a particle l′
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