Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

Abstract

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma -$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.

7 pages,RevTex, no figures Submitted to Phys.Rev.B

Cited by in corpus (44)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Emergence of quantum chaos in finite interacting Fermi systems
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
• Quantum Dynamics in Krylov Space: Methods and Applications
• Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
• Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
• Breit-Wigner width and participation ratio in finite interacting Fermi systems
• Relaxation theory for perturbed many-body quantum systems versus numerics and experiment
• Typicality of Prethermalization
• Perturbation Theory for the Rosenzweig-Porter Matrix Model
• Emergence of Quantum Ergodicity in Rough Billiards
• Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement
• Effective $\sigma$ Model Formulation for Two Interacting Electrons in a Disordered Metal
• Level Statistics and Localization for Two Interacting Particles in a Random Potential
• Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales
• On random symmetric matrices with a constraint: the spectral density of random impedance networks
• An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
• Few interacting particles in a random potential
• Two Interacting Electrons in a Quasiperiodic Chain
• Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
• Between Poisson and GUE statistics: Role of the Breit-Wigner width
• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
• Breit-Wigner width for two interacting particles in one-dimensional random potential
• Regularity and chaos in cavity QED
• Estimation of the Local Density of States on a Quantum Computer
• Typical relaxation of perturbed quantum many-body systems
• Refining Deutsch's approach to thermalization
• Random matrix ensembles with column/row constraints: part I
• Relaxation of isolated quantum systems beyond chaos
• Exploring integrability-chaos transition with a sequence of independent perturbations
• Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties
• Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
• Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
• Lyapunov decay in quantum irreversibility
• Critical Spectral Statistics at the Metal-Insulator Transition in Interacting Fermionic Systems
• Random sparse generators of Markovian evolution and their spectral properties
• Wavefunction extreme value statistics in Anderson localization
• Distribution of singular values of random band matrices; Marchenko-Pastur law and more
• Wannier basis method for KAM effect in quantum mechanics
• Non-Rayleigh signal of interacting quantum particles
• Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards
• Ergodic Properties of Local Spectral Density for a Conservative System of Coupled Quantum States
• Local Spectral Density for a Periodically Driven System of Coupled Quantum States with Strong Imperfection in Unperturbed Energies