Journal of Statistical Physics

, Volume 152, Issue 1, pp 93–111

Microscopic Structure of Shocks and Antishocks in the ASEP Conditioned on Low Current

Authors

  • V. Belitsky
    • Instituto de Matemática e EstatísticaUniversidade de São Paulo
    • Institute of Complex Systems IIForschungszentrum Jülich GmbH
    • Interdisziplinäres Zentrum für komplexe SystemeUniversität Bonn
Article

DOI: 10.1007/s10955-013-0758-0

Cite this article as:
Belitsky, V. & Schütz, G.M. J Stat Phys (2013) 152: 93. doi:10.1007/s10955-013-0758-0

Abstract

We study the time evolution of the ASEP on a one-dimensional torus with L sites, conditioned on an atypically low current up to a finite time t. For a certain one-parameter family of initial measures with a shock we prove that the shock position performs a biased random walk on the torus and that the measure seen from the shock position remains invariant. We compute explicitly the transition rates of the random walk. For the large scale behavior this result suggests that there is an atypically low current such that the optimal density profile that realizes this current is a hyperbolic tangent with a traveling shock discontinuity. For an atypically low local current across a single bond of the torus we prove that a product measure with a shock at an arbitrary position and an antishock at the conditioned bond remains a convex combination of such measures at all times which implies that the antishock remains microscopically stable under the locally conditioned dynamics. We compute the coefficients of the convex combinations.

Keywords

Asymmetric symmetric exclusion process Large deviations Shocks Antishocks

Copyright information

© Springer Science+Business Media New York 2013