{"title":"Exact moments for a run and tumble particle in a harmonic trap with a finite tumble time","authors":"Aoran Sun, Fangfu Ye, Rudolf Podgornik","doi":"arxiv-2409.00578","DOIUrl":null,"url":null,"abstract":"We study the problem of a run and tumble particle in a harmonic trap, with a\nfinite run and tumble time, by a direct integration of the equation of motion.\nAn exact 1D steady state distribution, diagram laws and a programmable Volterra\ndifference equation are derived to calculate any order of moments in any other\ndimension, both for steady state as well as the Laplace transform in time for\nthe intermediate states. We also use the moments to infer the distribution by\nconsidering a Gaussian quadrature for the corresponding measure, and from the\nscaling law of high order moments.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Statistical Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.00578","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
We study the problem of a run and tumble particle in a harmonic trap, with a
finite run and tumble time, by a direct integration of the equation of motion.
An exact 1D steady state distribution, diagram laws and a programmable Volterra
difference equation are derived to calculate any order of moments in any other
dimension, both for steady state as well as the Laplace transform in time for
the intermediate states. We also use the moments to infer the distribution by
considering a Gaussian quadrature for the corresponding measure, and from the
scaling law of high order moments.
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