Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.

@article{Pandey2017FiniterangeCG,
  title={Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.},
  author={Akhilesh Pandey and Avanish Kumar and Sanjay Puri},
  journal={Physical review. E},
  year={2017},
  volume={96 5-1},
  pages={
          052211
        }
}
Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of… 
3 Citations
Finite-range Coulomb gas models. II. Applications to quantum kicked rotors and banded random matrices.
TLDR
A Monte Carlo technique is developed to study finite-range Coulomb gas (FRCG) models, and it is demonstrated that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has range d=b-2/N=α^{2}/N, for N→∞.
Finite-range Coulomb gas models. I. Some analytical results.
TLDR
Finite-range Coulomb gas models are introduced as a generalization of the Dyson models with a finite range of eigenvalue interactions to provide a theoretical framework to study banded random matrices, and dynamical systems the matrix representation of which can be written in the form of banded matrices.
Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles.
TLDR
This work derives exact results for the distribution and average of the ratio of two consecutive level spacings in the Gaussian orthogonal to unitary crossover ensemble using a 3×3 random matrix model and applies this result to investigate the violation of time-reversal invariance in the quantum kicked rotor system.

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