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Phys Rev Lett. 2012 Apr 20;108(16):164101. Epub 2012 Apr 19.

Distributional response to biases in deterministic superdiffusion.

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Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan.


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 arcsine 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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