The non-equilibrium steady state of sparse systems

We study the steady state of a multiply-connected system that is driven out of equilibrium by a sparse perturbation [1]. The prototype example is an $N$-site ring coupled to a thermal bath, driven by a stationary source that induces transitions with log-wide distributed rates. An induced current arises, which is controlled by the strength of the driving. Due to the sparsity, the crossover from linear response to saturation becomes an intermediate regime where the current is exponentially small in $\sqrt{N}$, which is related to the work of Sinai on "random walk in a random environment". The expression for the energy absorption rate [2] reflects a crossover from linear to semi-linear response, and an additional topological term appears, that is correlated with the current. In the second part of the presentation I will expand on semi-linear response theory, relating to the simplest realistic application: the heating rate of cold atoms that are trapped in an optical billiard [3,4].

[1] D.Hurowitz, S.Rahav, D.Cohen, (EPL 2012, in press).

[2] D.Hurowitz, D.Cohen, (EPL 2011).

[3] A.Stotland, D.Cohen, N.Davidson (EPL 2009).

[4] A.Stotland, L.M.Pecora, D.Cohen (EPL 2010, PRE 2011).