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Cooling down Levy flights | I. Pavlyukevich
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26 Jan 2007 | Subject: | Statistical Mechanics | Abstract: | Let L(t) be a Levy flights process with a stability index alphain(0,2), and U be an external multi-well potential. A jump-diffusion Z satisfying a stochastic differential equation dZ(t)=-U’(Z(t-))dt+sigma(t)dL(t) describes an evolution of a Levy particle of an `instant temperature’ sigma(t) in an external force field. The temperature is supposed to decrease polynomially fast, i.e. sigma(t)approx t^{- heta} for some heta>0. We discover two different cooling regimes. If heta<1/alpha (slow cooling), the jump diffusion Z(t) has a non-trivial limiting distribution as t o infty, which is concentrated at the potential’s local minima. If heta>1/alpha (fast cooling) the Levy particle gets trapped in one of the potential wells. | Source: | arXiv, cond-mat/0701651 | Services: | Forum | Review | PDF | Favorites |
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