Non-Boltzmann Equilibrium Probability Densities for Non-Linear Lévy Oscillator
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 ≤ α≤ 2, and the potential energy x4. In particular, we show that the equilibrium PDF is bimodal and has power law asymptotics with the exponent -(α+3).
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