Universal correlations for deterministic plus random Hamiltonians

Abstract

We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $\phi$. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed H0 and for a class of probability distribution P$(\phi )$ of the random potential. We find a compact representation of the correlation function. From this representation one obtains readily the short distance behavior, which has been conjectured in various contexts to be universal. Indeed we find that it is totally independent of both H0 and P($\phi$).

26P, (+5 figures not included)

References in corpus (2)

• Correlation Functions in Disordered Systems
• Universality of Brezin and Zee's Spectral Correlator

Cited by in corpus (35)

• Cleaning large correlation matrices: tools from random matrix theory
• Non-Hermitean Random Matrix Theory: method of hermitization
• Universal singularity at the closure of a gap in a random matrix theory
• Level Spacing of Random Matrices in an External Source
• Spectral form factor in a random matrix theory
• Correlations of Nearby Levels Induced by a Random Potential
• Non-Gaussian Non-Hermitean Random Matrix Theory: phase transitions and addition formalism
• Nonhermitean Random Matrix Models
• An Extension of Level-spacing Universality
• Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem
• Rotational invariant estimator for general noisy matrices
• Law of addition in random matrix theory
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Infinite Products of Large Random Matrices and Matrix-valued Diffusion
• Crossover to Non-universal Microscopic Spectral Fluctuations in Lattice Gauge Theory
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Non-Hermitean Random Matrix Theory: Summation of Planar Diagrams, the "Single-Ring" Theorem and the Disk-Annulus Phase Transition
• Lectures on random matrix models. The Riemann-Hilbert approach
• Critical Scaling at Zero Virtuality in QCD
• Eigenvector dynamics under free addition
• Polynuclear growth model, GOE${}^2$ and random matrix with deterministic source
• Random matrices with external source and multiple orthogonal polynomials
• Adding and multiplying random matrices: a generalization of Voiculescu's formulae
• Eigenvalue spectra of asymmetric random matrices for multi-component neural networks
• Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials
• Density of State in a Complex Random Matrix Theory with External Source
• Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial
• Proof of a conjecture on the infinite dimension limit of a unifying model for random matrix theory
• Logarithmic moments of characteristic polynomials of random matrices
• Chaotic scattering through coupled cavities
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$
• A general and solvable random matrix model for spin decoherence
• Universality of S-matrix correlations for deterministic plus random Hamiltonians
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Asymptotic spectral independence of Wigner ensembles