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Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas

Sebastian Leitmann, Thomas Schwab, and Thomas Franosch*

  • Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria

  • *thomas.franosch@uibk.ac.at
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Phys. Rev. E 97, 022101 – Published 1 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022101

Abstract

We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.

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Phys. Rev. E 97, 022101– Published 1 February, 2018
  • Received 20 November 2017
  • Revised 19 December 2017
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