具有随机势的非线性Schroedinger方程的波包动力学
Dynamics of wave packets for the nonlinear Schroedinger equation with a random potential
摘要：
在非线性薛定谔方程的框架下，在无序的存在下，初始局域安德森模式的动力学进行了研究。结果表明，动力学可以描述的刘维尔算子的框架。用微扰法求出了初态动力学的波函数的解析表达式。从微扰解可以看出，初始定域的波函数仍然是定域的。在渐近大的时候，动力学可以定性描述的框架中的现象概率的方法，通过概率分布函数。它表明，概率分布函数可以由分数福克-普朗克方程，并对应于亚扩散。
英文摘要：
The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schroedinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator. An analytical expression for a wave function of the initial time dynamics is found by a perturbation approach. As follows from a perturbative solution the initially localized wave function remains localized. At asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function. It is shown that the probability distribution function may be governed by the fractional Fokker-Planck equation and corresponds to subdiffusion.
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