Universal spectral correlations in ensembles of random normal matrices

Abstract

We consider non-gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk to ring transition in the complex plane. We also show that the n-eigenvalue correlation and the spacing distribution are universal and identical to that of complex (Gaussian) Ginibre ensemble. Our results are confirmed by Monte Carlo calculations. We verify the universality for dissipative quantum kicked rotor system.

arXiv comment16 pages, 6 figures

References in corpus (13)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Truncations of random unitary matrices
• Random Matrices close to Hermitian or unitary: overview of methods and results
• Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
• On the structure of Normal Matrix Model
• Induced Ginibre ensemble of random matrices and quantum operations
• Large scale correlations in normal and general non-Hermitian matrix ensembles
• Spectral properties of the Google matrix of the World Wide Web and other directed networks
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Universal Cubic Eigenvalue Repulsion for Random Normal Matrices
• Quantum chaos and QCD at finite chemical potential
• Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials

Cited by in corpus (2)

• Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$
• A universal bound on Quantum Chaos from Random Matrix Theory