Escape by jumps and diffusion by α-stable noise across the barrier in a double well potential
arXiv (Cornell University)(2023)
摘要
Many physical and chemical phenomena are governed by stochastic escape across
potential barriers. The escape time depends on the structure of the noise and
the shape of the potential barrier. By applying α-stable noise from the
α=2 Gaussian noise limit to the α<2 jump processes, we find a
continuous transition of the mean escape time from the usual dependence on the
height of the barrier for Gaussian noise to a dependence solely on the width of
the barrier for α-stable noise. We consider the exit problem of a
process driven by α-stable noise in a double well potential. We study
individually the influences of the width and the height of the potential
barrier in the escape time and we show through scalings that the asymptotic
laws are described by a universal curve independent of both parameters. When
the dependence in the stability parameter is considered, we see that there are
two different diffusive regimes in which diffusion is described either by
Kramer's time or by the corresponding asymptotic law for α-stable noise.
We determine the regions of the noise parameter space in which each regime
prevails, and exploit this result to construct an anomalous example in which a
double well potential exhibit a different diffusion regime in each well for a
wide range of parameters.
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关键词
double well potential,barrier,diffusion,jumps
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