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Determinant Representation for Some Transition Probabilities in the TASEP with Second Class Particles

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Abstract

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.

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Authors and Affiliations

  1. Institut für Festkörperforschung, Forschungzentrum Jülich, 52425, Jülich, Germany

    Sakuntala Chatterjee & Gunter M. Schütz

  2. Physics Department, Technion, Haifa, 32000, Israel

    Sakuntala Chatterjee

Authors
  1. Sakuntala Chatterjee
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  2. Gunter M. Schütz
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Correspondence to Sakuntala Chatterjee.

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Chatterjee, S., Schütz, G.M. Determinant Representation for Some Transition Probabilities in the TASEP with Second Class Particles. J Stat Phys 140, 900–916 (2010). https://doi.org/10.1007/s10955-010-0022-9

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  • DOI: https://doi.org/10.1007/s10955-010-0022-9

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