Dynamical scaling for critical states: Validity of Chalker's ansatz for strong fractality

Article

关键词: DIAGONAL RANDOM MATRICES;    QUANTUM HALL SYSTEMS;    ANDERSON TRANSITION;    LOCALIZATION;    DIMENSIONS;    DIFFUSION;    ENSEMBLE;   

DOI  :  10.1103/PhysRevB.82.161102

来源: SCIE

【 摘 要 】

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 << 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 -> infinity and N/tau -> infinity, 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.

【 授权许可】

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