Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solution for eigenfunction statistics at the center-of-band
  anomaly in the Anderson localization model   An exact solution is found for the problem of the center-of-band ($E=0$)
anomaly in the one-dimensional (1D) Anderson model of localization. By deriving
and solving an equation for the generating function $\Phi(u,\phi)$ we obtained
an exact expression in quadratures for statistical moments $I_{q}=\langle
|\psi_{E}({\bf r})|^{2q}\rangle$ of normalized wavefunctions $\psi_{E}({\bf
r})$ which show violation of one-parameter scaling and emergence of an
additional length scale at $E\approx 0$.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga