Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multifractal dimensions for random matrices, chaotic quantum maps, and
  many-body systems   Multifractal dimensions allow for characterizing the localization properties
of states in complex quantum systems. For ergodic states the finite-size
versions of fractal dimensions converge to unity in the limit of large system
size. However, the approach to the limiting behavior is remarkably slow. Thus,
an understanding of the scaling and finite-size properties of fractal
dimensions is essential. We present such a study for random matrix ensembles,
and compare with two chaotic quantum systems --- the kicked rotor and a spin
chain. For random matrix ensembles we analytically obtain the finite-size
dependence of the mean behavior of the multifractal dimensions, which provides
a lower bound to the typical (logarithmic) averages. We show that finite
statistics has remarkably strong effects, so that even random matrix
computations deviate from analytic results (and show strong sample-to-sample
variation), such that restoring agreement requires exponentially large sample
sizes. For the quantized standard map (kicked rotor) the multifractal
dimensions are found to follow the random matrix predictions closely, with the
same finite statistics effects. For a XXZ spin-chain we find significant
deviations from the random matrix prediction --- the large-size scaling follows
a system-specific path towards unity. This suggests that local many-body
Hamiltonians are "weakly ergodic", in the sense that their eigenfunction
statistics deviate from random matrix theory.

1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph