Return probability and scaling exponents in the critical random matrix ensemble

Details Return probability and scaling exponents in the critical random matrix ensemble Return probability and scaling exponents in the critical random matrix ensemble

2011-04-19

arxiv.org/abs/1104.3872v1

J. Phys. A: Math. Theor. 44 (2011) 305003

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, submitted to J. Phys. A

Scientific paper

10.1088/1751-8113/44/30/305003

We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large system size. Using the supersymmetric virial expansion we confirm the scaling law and find analytical expressions for the fractal dimension of the wave functions $d_2$ and the dynamical scaling exponent $\mu$. By comparing them we verify the validity of the Chalker's ansatz for dynamical scaling.

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