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Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux

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Abstract

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is z=1 rather than the KPZ exponent z=3/2 which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.

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Authors and Affiliations

  1. Dipartimento di Fisica “E.R. Caianiello”, and Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia (CNISM), Università di Salerno, Fisciano, Italy

    V. Popkov

  2. Interdisziplinäres Zentrum für Komplexe Systeme, Universität Bonn, Brühler Straße 7, 53119, Bonn, Germany

    V. Popkov & G. M. Schütz

  3. Institut für Festkörperforschung, Forschungszentrum Jülich, 52425, Jülich, Germany

    G. M. Schütz

Authors
  1. V. Popkov
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  2. G. M. Schütz
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Correspondence to V. Popkov.

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Popkov, V., Schütz, G.M. Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux. J Stat Phys 142, 627–639 (2011). https://doi.org/10.1007/s10955-011-0137-7

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  • DOI: https://doi.org/10.1007/s10955-011-0137-7

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