Distributional Response to Biases in Deterministic Superdiffusion

Abstract

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.

13 pages, 5 figures

References in corpus (7)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary
• Weakly non-ergodic Statistical Physics
• Nonergodisity of a time series obeying Lévy statistics
• Universality of algebraic laws in Hamiltonian systems
• Universal fluctuations in subdiffusive transport
• Calculation of Superdiffusion for the Chirikov-Taylor Model

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