Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subdiffusion in classical and quantum nonlinear Schr\"odinger equations
  with disorder   The review is concerned with the nonlinear Schr\"odinger equation (NLSE) in
the presence of disorder. Disorder leads to localization in the form of the
localized Anderson modes (AM), while nonlinearity is responsible for the
interaction between the AMs and transport. The dynamics of an initially
localized wave packets are concerned in both classical and quantum cases. In
both cases, there is a subdiffusive spreading, which is explained in the
framework of a continuous time random walk (CTRW), and it is shown that
subdiffusion is due to the transitions between those AMs, which are strongly
overlapped. This overlapping being a common feature of both classical and
quantum dynamics, leads to the clustering with an effective trapping of the
wave packet inside each cluster. Therefore, the dynamics of the wave packet
corresponds to the CTRW, where the basic mechanism of subdiffusion is an
entrapping of the wave packet with delay, or waiting, times distributed by the
power law $w(t)\sim 1/t^{1+\alpha}$, where $\alpha$ is the transport exponent.
It is obtained that $\alpha=1/3$ for the classical NLSE and $\alpha=1/2$ for
the quantum NLSE.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph