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arxiv: cond-mat/0012155 · v1 · submitted 2000-12-09 · ❄️ cond-mat.stat-mech

Non-Boltzmann Equilibrium Probability Densities for Non-Linear L\'{e}vy Oscillator

A. Chechkin (Institute for Theoretical Physics , Kharkov , Ukraine) , V. Gonchar (Institute for Theoretical Physics , R. Gorenflo (Department of Mathematics , Computer Science , Free University of Berlin , Berlin
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Germany) F. Mainardi (Department of Physics University of Bologna Bologna Italy) L. Tanatarov (Institute for Theoretical Physics
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classification ❄️ cond-mat.stat-mech
keywords alphaequilibriumnon-linearoscillatorprobabilityanalyticallyasymptoticsbimodal
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We study, both analytically and by numerical modeling the equilibrium probability density function for an non-linear L\'{e}vy oscillator with the L\'{e}vy index \alpha, 1 \leq \alpha \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 -(\alpha +3).

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