Gaussian random-matrix process and universal parametric correlations in complex systems

Journal Article · Wed Nov 01 04:00:00 EST 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.52.4776· OSTI ID:127588

Attias, H; Alhassid, Y ^[1]

---

1. Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)

We introduce the framework of the Gaussian random-matrix process as an extension of Dyson`s Gaussian ensembles and use it to discuss the statistical properties of complex quantum systems that depend on an external parameter. We classify the Gaussian processes according to the short-distance diffusive behavior of their energy levels and demonstrate that all parametric correlation functions become universal upon the appropriate scaling of the parameter. The class of differentiable Gaussian processes is identified as the relevant one for most physical systems. We reproduce the known spectral correlators and compute eigenfunction correlators in their universal form. Numerical evidence from both a chaotic model and weakly disordered model confirms our predictions.

• Research Organization: Yale University
• DOE Contract Number: FG02-91ER40608
• OSTI ID: 127588
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 52; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CORRELATIONS
GAUSS FUNCTION
MATRIX ELEMENTS
PARAMETRIC ANALYSIS
QUANTUM MECHANICS