Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-ergodic delocalized phase in Anderson model on Bethe lattice and
  regular graph   We develop a novel analytical approach to the problem of single particle
localization in infinite dimensional spaces such as Bethe lattice and random
regular graphs. The key ingredient of the approach is the notion of the
inverted order thermodynamic limit (IOTL) in which the coupling to the
environment goes to zero before the system size goes to infinity. Using IOTL
and Replica Symmetry Breaking (RSB) formalism we derive analytical expressions
for the fractal dimension D_{1} that distinguishes between the extended
ergodic, D_{1}=1, and extended non-ergodic (multifractal), 0<D_{1}<1 states on
the Bethe lattice and random regular graphs with the branching number K. We
also employ RSB formalism to derive the analytical expression
ln(1/S_{typ})~(W_{c}-W)^{-1} for the typical imaginary part of self-energy
S_{typ} in the non-ergodic phase close to the Anderson transition in the
conventional thermodynamic limit. We prove the existence of an extended
non-ergodic phase in a broad range of disorder strength and energy and
establish the phase diagrams of the models as a function of disorder and
energy. The results of the analytical theory are compared with large-scale
population dynamics and with the exact diagonalization of Anderson model on
random regular graphs. We discuss the consequences of these results for the
many body localization.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs