Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-08-16
Phys. Rev. B 82, 161102(R) (2010)
Physics
Condensed Matter
Disordered Systems and Neural Networks
4 pages, 1 figure
Scientific paper
10.1103/PhysRevB.82.161102
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.
Cuevas Emilio
Kravtsov Vladimir E.
Ossipov Alexander
Yevtushenko O. M.
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