Nonlinear Response in the Driven Lattice Lorentz Gas
Nonlinear Response in the Driven Lattice Lorentz Gas
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DOI：
10.1103/physrevlett.111.190603
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发表时间：
2013-11-05
影响因子：
8.6
通讯作者：
Franosch, Thomas
中科院分区：
文献类型：
--
作者：
Leitmann, Sebastian;Franosch, Thomas
当力被打开时，我们确定了具有随机分布的硬障碍物的晶格上的示踪剂的非线性时间相关响应。该计算精确到障碍物密度的一阶，并且适用于任意大的力。然而，在无杂质晶格上，稳态下的非线性漂移速度在驱动力中是解析的，与杂质的相互作用引入了超出线性范围的对数贡献。对于任何有限的力值，速度向稳态的长时间衰减都是指数快的，这与线性响应中预测的幂律松弛形成鲜明对比。我们通过与随机模拟进行比较来讨论分析结果的有效性范围。
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.