The steady-state correlation characteristics of superdiffusion in the form of Levy flights in one-dimensional confinement potential profiles are investigated both theoretically and numerically. Specifically, for Cauchy stable noise we calculate the steady-state probability density function for an infinitely deep rectangular potential well and for a symmetric steep potential well of the type U(x)∞x2m. For these potential profiles and arbitrary Levy index α, we obtain the asymptotic expression of the spectral power density.
Kharcheva, A., Dubkov, A., Dybiec, B., Spagnolo, B., Valenti, D. (2016). Spectral characteristics of steady-state Lévy flights in confinement potential profiles. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2016(5), 054039-1-054039-13 [10.1088/1742-5468/2016/05/054039].
Spectral characteristics of steady-state Lévy flights in confinement potential profiles
SPAGNOLO, Bernardo
;VALENTI, Davide
2016-01-01
Abstract
The steady-state correlation characteristics of superdiffusion in the form of Levy flights in one-dimensional confinement potential profiles are investigated both theoretically and numerically. Specifically, for Cauchy stable noise we calculate the steady-state probability density function for an infinitely deep rectangular potential well and for a symmetric steep potential well of the type U(x)∞x2m. For these potential profiles and arbitrary Levy index α, we obtain the asymptotic expression of the spectral power density.
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