论文标题
在浅外部电势中缺乏分数布朗运动的限制和非螺栓固定状态
Absence of confinement and non-Boltzmann stationary states of fractional Brownian motion in shallow external potentials
论文作者
论文摘要
我们研究粒子在表格$ u（x）= | x |^c $（$ 0 <c <2 $）的亚谐波电位中的扩散运动，该运动是由远程相关的，固定的固定分数高斯噪声$ 0 <α\ le2 $驱动的。在没有电势的情况下，粒子表现出具有异常扩散指数$α$的游离分数布朗运动。尽管对于谐波外部电位，动力学会收敛到高斯固定状态，但从广泛的数值分析中，我们在这里证明，与谐波电位相比，较浅的固定状态仅在关系$ c> 2（1-1/α）$所持的时间内就存在。我们根据平方平均位移分析运动，并且（当存在）固定概率密度函数（PDF）。此外，我们讨论了在浅外部电势中的L {é} vy飞行的非平稳性的类比。
We study the diffusive motion of a particle in a subharmonic potential of the form $U(x)=|x|^c$ ($0<c<2$) driven by long-range correlated, stationary fractional Gaussian noise $ξ_α(t)$ with $0<α\le2$. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent $α$. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation $c>2(1-1/α)$ holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function (PDF). Moreover we discuss analogies of non-stationarity of L{é}vy flights in shallow external potentials.
