Finite-Range Coulomb Gas Models I: Some Analytical Results
arXiv:1905.10524 · doi:10.1103/PhysRevE.101.022217
Abstract
Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas (FRCG) models as a generalization of the Dyson models with a finite range of eigenvalue interactions. As the range of interaction increases, there is a transition from Poisson statistics to classical random matrix statistics. These models yield new universality classes of random matrix ensembles. They also provide a theoretical framework to study banded random matrices, and dynamical systems whose matrix representation can be written in the form of banded matrices.
References in corpus (12)
- Random-Matrix Theory of Quantum Transport
- Random Matrix Theories in Quantum Physics: Common Concepts
- Noise Dressing of Financial Correlation Matrices
- Universal and non-universal properties of cross-correlations in financial time series
- Statistics of energy levels and eigenfunctions in disordered systems
- Transition to chaos in random networks with cell-type-specific connectivity
- Short-range plasma model for intermediate spectral statistics
- An exactly solvable many-body problem in one dimension
- Random Matrix Model for Nakagami-Hoyt Fading
- Finite-Range Coulomb Gas Models II: Applications to Quantum Kicked Rotors and Banded Random Matrices
- Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors
- A lecture on the Calogero-Sutherland models
Cited by in corpus (7)
- Model of level statistics for disordered interacting quantum many-body systems
- Particles confined in arbitrary potentials with a class of finite-ranged interactions
- Finite-Range Coulomb Gas Models II: Applications to Quantum Kicked Rotors and Banded Random Matrices
- Spectral form factor and energy correlations in banded random matrices
- Crossover in densities of confined particles with finite range of interaction
- Level dynamics and avoided level crossings in driven disordered quantum dots
- Enhancement in Breaking of Time-reversal Invariance in the Quantum Kicked Rotor