Parametric spectral correlations in disordered and chaotic structures

Abstract

We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the (n,m)-point parametric correlation function of the initial and final density of states for perturbations of arbitrary rank and strength. A further generalization of these results allows for the incorporation of short-range spatial correlations in diffusive as well as ballistic chaotic structures.

4 pages, 1 figure

References in corpus (3)

• The Statistical Theory of Quantum Dots
• Quantum Effects in Coulomb Blockade
• Wave function correlations on the ballistic scale: Exploring quantum chaos by quantum disorder

Cited by in corpus (7)

• Tunable Fermi-Edge Resonance in an Open Quantum Dot
• Fermi Edge Singularities in the Mesoscopic Regime: I. Anderson Orthogonality Catastrophe
• Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem
• Parametric Spectral Statistics in Unitary Random Matrix Ensembles: From Distribution Functions to Intra-Level Correlations
• Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials
• Parametric Statistics of Individual Energy Levels in Random Hamiltonians
• Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra