Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Fluctuations in Spectra of Disordered Systems at the Anderson
  Transition   Using the level--spacing distribution and the total probability function of
the numbers of levels in a given energy interval we analyze the crossover of
the level statistics between the delocalized and the localized regimes. By
numerically calculating the electron spectra of systems of up to $32^3$ lattice
sites described by the Anderson Hamiltonian it is shown that the distribution
$P(s)$ of neighboring spacings is {\em scale- independent} at the
metal-insulator transition. For large spacings it has a Poisson-like asymptotic
form $P(s)\propto \exp (- A\,s/\Delta )$, where $A \approx 1.9$. At the
critical point we obtain a linear relationship between the variance of the
number of levels $\langle [\delta n(\varepsilon)]^2 \rangle $ and their average
number $\langle n(\varepsilon)\rangle $ within the interval $\varepsilon$. The
constant of proportionality is less than unity due to the repulsion of the
levels. Both $P(s)$ and $\langle [\delta n(\varepsilon)]^2 \rangle $ are
determined by the probability density $Q_{n}(\varepsilon)$ of having exactly
$n$ levels in the energy interval $\varepsilon $. The distribution
$Q_{n}(\varepsilon)$ at the critical point is found to be size--independent and
to obey a Gaussian law near its maximum, where $n\sim \langle n \rangle $.

16
The categories of this paper are: stat
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th