Cooling Down Lévy Flights
نویسنده
چکیده
Let L(t) be a Lévy flights process with a stability index α ∈ (0, 2), and U be an external multiwell potential. A jump-diffusion Z satisfying a stochastic differential equation dZ(t) = −U ′(Z(t−))dt+ σ(t)dL(t) describes an evolution of a Lévy particle of an ‘instant temperature’ σ(t) in an external force field. The temperature is supposed to decrease polynomially fast, i.e. σ(t) ≈ t for some θ > 0. We discover two different cooling regimes. If θ < 1/α (slow cooling), the jump diffusion Z(t) has a non-trivial limiting distribution as t → ∞, which is concentrated at the potential’s local minima. If θ > 1/α (fast cooling) the Lévy particle gets trapped in one of the potential wells. PACs numbers: 05.40.Fb, 02.50.Ey, 02.50.Fz, 02.50.Ga
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