Summing graphs for random band matrices

Abstract

A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix model regularization of 2d-gravity, turns out to be very useful for band matrices. The critical behavior at the edge of spectrum and the asymptotics of energy level correlation function are considered. This correlation function together with the hypothesis about universality of spectral correlations allows to estimate easily the localization length for eigen-vectors. A smoothed two-point correlation function of local density of states $\overline{\rho (E_1,i)\rho (E_2,j{)}_c}$ as well as the energy level correlation for finite size band matrices are also found. As d-dimensional generalization of band matrices lattice Hamiltonians with long-range random hopping are considered as well.

20 pages, REVTEX, 11 eps figures, improved version accepted for publication in Phys. Rev. E

References in corpus (4)

• Chaos {\sl vs} Thermalization in the Nuclear Shell Model
• Correlation Functions in Disordered Systems
• SPECTRAL CORRELATIONS IN DISORDERED ELECTRONIC SYSTEMS: CROSSOVER FROM METAL TO INSULATOR REGIME
• Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlevé again.

Cited by in corpus (10)

• Duality of Orthogonal and Symplectic Matrix Integrals and Quaternionic Feynman Graphs
• The Altshuler-Shklovskii Formulas for Random Band Matrices I: the Unimodular Case
• Scaling Properties of Multilayer Random Networks
• Transfer matrices, non-Hermitian Hamiltonians and Resolvents: some spectral identities
• Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties
• Moments of vicious walkers and Möbius graph expansions
• Partial chord diagrams and matrix models
• Real symmetric random matrices and paths counting
• Phase transitions and random matrices
• On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles