Perturbation approach to multifractal dimensions for certain critical random-matrix ensembles.

摘要: Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series the regimes strong and weak multifractality. In both regimes, we obtain expressions similar to those banded ensemble extensively discussed literature. For certain ensembles, leading-order term multifractality can be calculated within standard theory. other models, such a direct approach requires modifications, which briefly discussed. Our analytical formulas good agreement with numerical calculations.