Yuste S B, Oshanin G, Lindenberg K, Bénichou O, Klafter J
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 1):021105. doi: 10.1103/PhysRevE.78.021105. Epub 2008 Aug 7.
We study the long-time tails of the survival probability P(t) of an A particle diffusing in d-dimensional media in the presence of a concentration rho of traps B that move subdiffusively, such that the mean square displacement of each trap grows as tgamma with 0 < or = gamma < or =1. Starting from a continuous time random walk description of the motion of the particle and of the traps, we derive lower and upper bounds for P(t) and show that for gamma < or =2/(d+2) these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving A particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For gamma >2/(d+2) and d< or =2 the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For d>2 , however, the upper and lower bounds in this gamma regime no longer coincide, and the decay law for the survival probability of the A particle remains ambiguous.
我们研究了在存在浓度为(\rho)的亚扩散移动陷阱(B)的情况下，(d)维介质中(A)粒子扩散的生存概率(P(t))的长时间尾部，其中每个陷阱的均方位移随(t^{\gamma})增长，(0\leqslant\gamma\leqslant1)。从粒子和陷阱运动的连续时间随机游走描述出发，我们推导了(P(t))的上下界，并表明当(\gamma\leqslant\frac{2}{d + 2})时，这些界渐近重合，从而确定了渐近精确结果。在这个区域的渐近衰减规律与固定陷阱的情况完全相同。这意味着对于足够亚扩散的陷阱，移动的(A)粒子基本上将陷阱视为固定的，利夫希茨或捕获尾部保持不变。当(\gamma>\frac{2}{d + 2})且(d\leqslant2)时，上下界再次重合，导致衰减规律与静止粒子的相同。因此，在这个区域，移动的陷阱基本上将粒子视为固定的。然而，对于(d>2)，在这个(\gamma)区域的上下界不再重合，(A)粒子生存概率的衰减规律仍然不明确。
