Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Ergodicity on Graphs : from Spectral to Spatial Delocalization   We prove a quantum-ergodicity theorem on large graphs, for eigenfunctions of
Schr\"odinger operators in a very general setting. We consider a sequence of
finite graphs endowed with discrete Schr\"odinger operators, assumed to have a
local weak limit. We assume that our graphs have few short loops, in other
words that the limit model is a random rooted tree endowed with a random
discrete Schr\"odinger operator. We show that absolutely continuous spectrum
for the infinite model, reinforced by a good control of the moments of the
Green function, imply "quantum ergodicity", a form of spatial delocalization
for eigenfunctions of the finite graphs approximating the tree. This roughly
says that the eigenfunctions become equidistributed in phase space. Our result
applies in particular to graphs converging to the Anderson model on a regular
tree, in the r\'egime of extended states studied by Klein and Aizenman-Warzel.

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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
3
The categories of this paper are: physics
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org