Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusion in the mean for a periodic Schr\"{o}dinger equation perturbed
  by a fluctuating potential   We consider the evolution of a quantum particle hopping on a cubic lattice in
any dimension and subject to a potential consisting of a periodic part and a
random part that fluctuates stochastically in time. If the random potential
evolves according to a stationary Markov process, we obtain diffusive scaling
for moments of the position displacement, with a diffusion constant that grows
as the inverse square of the disorder strength at weak coupling. More
generally, we show that a central limit theorem holds such that the square
amplitude of the wave packet converges, after diffusive rescaling, to a
solution of a heat equation.

19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th