{"title":"在ℤ上具有长程跳跃的多物种非对称简单排斥过程的积分性","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":"{\"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}","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
摘要
让我们考虑一个在 Z 上有有限多个粒子的双面多物种随机粒子模型，其定义如下。假设每个粒子都用一个正整数 l 标记，并等待速率为 1 的指数分布的随机时间。然后，它以 p 的概率选择向右跳，或以 q=1-p 的概率选择向左跳。如果粒子选择向右跳，它就会跳到离它最近的、被粒子 l′本文章由计算机程序翻译，如有差异，请以英文原文为准。
Integrability of the Multi-Species Asymmetric Simple Exclusion Processes with Long-Range Jumps on ℤ
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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