Density of states in the non-hermitian Lloyd model

Abstract

We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find the localization length from the density of states of a non-hermitian random ``Hamiltonian''. However, finding the density of states of a non-hermitian random ``Hamiltonian'' remains an open problem, contrary to previous findings in the literature.

6 pages, RevTex, two-columns

References in corpus (12)

• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian Localization and Population Biology
• Non-Hermitean Random Matrix Theory: method of hermitization
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Directed Quantum Chaos
• Theory of directed localization in one dimension
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Quantum Disordered Systems with a Direction
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics
• Non-Hermitean De-Localization: Multiple Scattering and Bounds
• Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors
• A Non-Hermitean Particle in a Disordered World

Cited by in corpus (26)

• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• Non-Hermitean Localization and De-Localization
• Dynamical response of a pinned two-dimensional Wigner crystal
• Dynamical response of a weakly pinned two-dimensional Wigner crystal
• Fundamental limits for reciprocal and non-reciprocal non-Hermitian quantum sensing
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Spectral Curves of Non-Hermitean Hamiltonians
• Non-Hermitian spectra and Anderson localization
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Enumeration of simple random walks and tridiagonal matrices
• Spectral duality and distribution of exponents for transfer matrices of block tridiagonal Hamiltonians
• Transverse Meissner Physics of Planar Superconductors with Columnar Pins
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Interaction effects in non-Hermitian models of vortex physics
• Two-dimensional Non-Hermitian Delocalization Transition as a Probe for the Localization Length
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Effective impurity behavior emergent from non-Hermitian proximity effect
• Optical properties of quantum wires: Disorder-scattering in the Lloyd-model
• A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems
• Random-phase reservoir and a quantum resistor: The Lloyd model
• Optimal Fluctuations and Tail States of non-Hermitian Operators
• Theory of Localization in a Disordered Ring in a Non-Hermitian Field
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Non-Hermitian tridiagonal random matrices and returns to the origin of a random walk