Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical scaling for critical states: is Chalker's ansatz valid for
  strong fractality?   The dynamical scaling for statistics of critical multifractal eigenstates
proposed by Chalker is analytically verified for the critical random matrix
ensemble in the limit of strong multifractality controlled by the small
parameter $b\ll 1$. The power law behavior of the quantum return probability
$P_{N}(\tau)$ as a function of the matrix size $N$ or time $\tau$ is confirmed
in the limits $\tau/N\rightarrow\infty$ and $N/\tau\rightarrow\infty$,
respectively, and it is shown that the exponents characterizing these power
laws are equal to each other up to the order $b^{2}$. The corresponding
analytical expression for the fractal dimension $d_{2}$ is found.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc