Levy Diffusion and Classes of Universal Parametric Correlations

Abstract

A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be labeled by a parameter $\alpha \in (0,2]$, in a manner analogous to Lévy diffusion. Universality is obtained after scaling by the (anomalous) diffusion constant $D_{\alpha }$ (the usual scaling is divergent for $\alpha <2$). For each $\alpha$, correlation functions are universal, and distinct. The previous results in the literature correspond to the limiting case of superdiffusion, $\alpha =2$.

4 pages, uuencoded and compressed postscript

References in corpus (1)

• "Level Curvature" Distribution for Diffusive Aharonov-Bohm Systems: analytical results

Cited by in corpus (6)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Quantum Lévy Processes and Fractional Kinetics
• Invariant Correlation Entropy and Complexity of Quantum States
• Turbulent-like Diffusion in Complex Quantum Systems
• Universal Predictions for Statistical Nuclear Correlations
• Topological Dependence of Universal Correlations in Multi-Parameter Hamiltonians