Analytical Results for Random Band Matrices with Preferential Basis

Abstract

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a random band matrix with a strongly fluctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of random band matrices with preferential basis. Our analytical results are in good agreement with (but more general than) recent numerical findings by Jacquod and Shepelyansky.

8 pages RevTex and 1 Figure, both uuencoded

References in corpus (2)

• Scaling in Interaction-Assisted Coherent Transport
• $h/2e$--Oscillations for Correlated Electron Pairs in Disordered Mesoscopic Rings

Cited by in corpus (26)

• 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
• Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
• Breit-Wigner width and participation ratio in finite interacting Fermi systems
• Quasi-Particle Bound States around Impurities in d-wave Superconductors
• 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
• Localized to extended states transition for two interacting particles in a two-dimensional random potential
• Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales
• An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
• Few interacting particles in a random potential
• 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
• Breit-Wigner width for two interacting particles in one-dimensional random potential
• Disorder and Two-Particle Interaction in Low-Dimensional Quantum Systems
• Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties
• Exploring integrability-chaos transition with a sequence of independent perturbations
• Critical Spectral Statistics at the Metal-Insulator Transition in Interacting Fermionic Systems
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• 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