Distributional Response to Biases in Deterministic Superdiffusion

Details Distributional Response to Biases in Deterministic Superdiffusion Distributional Response to Biases in Deterministic Superdiffusion

2011-12-23

arxiv.org/abs/1112.5521v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 5 figures

Scientific paper

We report on a novel response to biases in deterministic superdiffusion. For its reduced map, we show using infinite ergodic theory that the time-averaged velocity (TAV) is intrinsically random and its distribution obeys the generalized arc-sine distribution. A distributional limit theorem indicates that the TAV response to a bias appears in the distribution, which is an example of what we term a distributional response induced by a bias. Although this response in single trajectories is intrinsically random, the ensemble-averaged TAV response is linear.

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