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| I present results on the ballistic and diffusive behavior of Langevin dynamics under a space-time periodic driving force. In the hyperbolic scaling, a non-trivial average velocity can be observed even if the external forcing vanishes. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level -- a phenomenon called negative mobility. The diffusive limit of (possibly strongly) forced systems is studied using appropriate solutions of Poisson equations, extending recent works on pointwise estimates of the resolvent for the generator associated with Langevin dynamics. |
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