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Non-Boltzmann Equilibrium Probability Densities for Non-Linear Lévy Oscillator

A. Chechkin·V. Gonchar·R. Gorenflo·F. Mainardi·L. Tanatarov
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Abstract

We study, both analytically and by numerical modeling the equilibrium probability density function for an non-linear Lévy oscillator with the Lévy index α, 1 \leq α\leq 2, and the potential energy x^4. In particular, we show that the equilibrium PDF is bimodal and has power law asymptotics with the exponent -(α+3).

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A. Chechkin, V. Gonchar, R. Gorenflo, F. Mainardi, L. Tanatarov. 2000-12-09. Non-Boltzmann Equilibrium Probability Densities for Non-Linear Lévy Oscillator. https://arxiv.org/abs/cond-mat/0012155

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