Hybridization of wave functions in one-dimensional localization

Abstract

A quantum particle can be localized in a disordered potential, the effect known as Anderson localization. In such a system, correlations of wave functions at very close energies may be described, due to Mott, in terms of a hybridization of localized states. We revisit this hybridization description and show that it may be used to obtain quantitatively exact expressions for some asymptotic features of correlation functions, if the tails of the wave functions and the hybridization matrix elements are assumed to have log-normal distributions typical for localization effects. Specifically, we consider three types of one-dimensional systems: a strictly one-dimensional wire and two quasi-one-dimensional wires with unitary and orthogonal symmetries. In each of these models, we consider two types of correlation functions: the correlations of the density of states at close energies and the dynamic response function at low frequencies. For each of those correlation functions, within our method, we calculate three asymptotic features: the behavior at the logarithmically large "Mott length scale", the low-frequency limit at length scale between the localization length and the Mott length scale, and the leading correction in frequency to this limit. In the several cases, where exact results are available, our method reproduces them within the precision of the orders in frequency considered.

10 pages, 5 figures. Several references added, minor corrections corresponding to the journal version

References in corpus (3)

• Local correlations of different eigenfunctions in a disordered wire
• Commensurability effects in one-dimensional Anderson localization: anomalies in eigenfunction statistics
• Correlations of the local density of states in quasi-one-dimensional wires

Cited by in corpus (14)

• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Suppression of Interactions in Multimode Random Lasers in the Anderson Localized Regime
• Resonant energy scales and local observables in the many-body localised phase
• Length scales in the many-body localized phase and their spectral signatures
• Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian
• Mott, Floquet, and the response of periodically driven Anderson insulators
• Dielectric response of Anderson and pseudogapped insulators
• Spectral correlations in Anderson insulating wires
• Wave function correlations and the AC conductivity of disordered wires beyond the Mott-Berezinskii law
• Low-energy dynamical response of an Anderson insulator with local attraction
• Superconducting proximity effect in quantum wires without time-reversal symmetry
• Spectral correlations in finite-size Anderson insulators
• Density of reflection resonances in one-dimensional disordered Schrödinger operators
• Anderson localization of a Majorana fermion