Nonlinear Response in the Driven Lattice Lorentz Gas

Sebastian Leitmann; Thomas Franosch

doi:10.1103/physrevlett.111.190603

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arXiv · 1311.1321

Nonlinear Response in the Driven Lattice Lorentz Gas

Sebastian Leitmann·Thomas Franosch

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Abstract

We determine the nonlinear time-dependent response of a tracer on a lattice with randomly distributed hard obstacles as a force is switched on. The calculation is exact to first order in the obstacle density and holds for arbitrarily large forces. Whereas, on the impurity-free lattice, the nonlinear drift velocity in the stationary state is analytic in the driving force, interactions with impurities introduce logarithmic contributions beyond the linear regime. The long-time decay of the velocity toward the steady state is exponentially fast for any finite value of the force, in striking contrast to the power-law relaxation predicted within linear response. We discuss the range of validity of our analytic results by comparison to stochastic simulations.

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Sebastian Leitmann, Thomas Franosch. 2013-11-06. Nonlinear Response in the Driven Lattice Lorentz Gas. https://doi.org/10.1103/physrevlett.111.190603

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