Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective confining potential of quantum states in disordered media   The amplitude of localized quantum states in random or disordered media may
exhibit long range exponential decay. We present here a theory that unveils the
existence of an effective potential which finely governs the confinement of
these states. In this picture, the boundaries of the localization subregions
for low energy eigenfunctions correspond to the barriers of this effective
potential, and the long range exponential decay characteristic of Anderson
localization is explained as the consequence of multiple tunneling in the dense
network of barriers created by this effective potential. Finally, we show that
the Weyl's formula based on this potential turns out to be a remarkable
approximation of the density of states for a large variety of one-dimensional
systems, periodic or random.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc