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TASEP speed process: an effective medium approach

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dc.contributor.author KUMAR, AANJANEYA en_US
dc.contributor.author DHAR, DEEPAK en_US
dc.date.accessioned 2020-04-03T17:22:42Z
dc.date.available 2020-04-03T17:22:42Z
dc.date.issued 2020-01 en_US
dc.identifier.citation Journal of Statistical Mechanics: Theory and Experiment, 2020. en_US
dc.identifier.issn 1742-5468 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4527
dc.identifier.uri https://doi.org/10.1088/1742-5468/ab5b8a en_US
dc.description.abstract We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at the origin and to its left, all sites are occupied with first class particles while to its right, all sites are vacant. Ferrari and Kipnis proved that in any particular realization, the average velocity of the second class particle tends to a constant, but this mean value has a wide variation in different histories. We discuss this phenomena, here called the TASEP speed process, in an approximate effective medium description, in which the second class particle moves in a random background of the space-time dependent average density of the first class particles. We do this in three different approximations of increasing accuracy, treating the motion of the second-class particle, always in continuous time, first as a simple biassed random walk in a continuum Langevin equation description, then as a biassed Markovian random walk on a lattice with space and time dependent jump rates, and finally as a Non-Markovian biassed walk on a lattice, with a non-exponential distribution of waiting times between jumps. We find that, when the displacement at time T is x 0, the conditional expectation of displacement, at time zT (z  >  1) is zx 0, and the variance of the displacement only varies as . We extend this approach to describe the trajectories of a tagged particle in the case of a finite lattice, where there are L classes of particles on an L-site line, initially placed in the order of increasing class number. Lastly, we discuss a variant of the problem in which the exchanges between adjacent particles happened at rates proportional to a power of the difference in their class numbers. en_US
dc.language.iso en en_US
dc.publisher IOP Publishing en_US
dc.subject Physics en_US
dc.subject TOC-APR-2020 en_US
dc.subject 2020 en_US
dc.subject 2020-MAR-WEEK5 en_US
dc.title TASEP speed process: an effective medium approach en_US
dc.type Article en_US
dc.contributor.department Dept. of Physics en_US
dc.identifier.sourcetitle Journal of Statistical Mechanics: Theory and Experiment en_US
dc.publication.originofpublisher Foreign en_US


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