Delocalization in an open one-dimensional chain in an imaginary vector potential

Abstract

We present first results for the transmittance, T, through a 1D disordered system with an imaginary vector potential, ih, which provide a new analytical criterion for a delocalization transition in the model. It turns out that the position of the critical curve on the complex energy plane (i.e. the curve where an exponential decay of <T> is changed by a power-law one) is different from that obtained previously from the complex energy spectra. Corresponding curves for <T^n> or <ln T> are also different. This happens because of different scales of the exponential decay of one-particle Green's functions (GF) defining the spectra and many-particle GF governing transport characteristics, and reflects higher-order correlations in localized eigenstates of the non-Hermitian model.

4 pages in RevTex, 1 eps figure included

References in corpus (8)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Non-Hermitian Delocalization and Eigenfunctions
• Eigenvector statistics in non-Hermitian random matrix ensembles
• Delocalization in coupled one-dimensional chains
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics
• Density of states in the non-hermitian Lloyd model
• Localization in an imaginary vector potential

Cited by in corpus (18)

• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Non-Hermitian skin effect beyond the tight-binding models
• Non-Hermitian bidirectional robust transport
• Localization-delocalization transition in disordered systems with a direction
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Erratic non-Hermitian skin localization
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Tight-binding lattices with an oscillating imaginary gauge field
• Controllable unidirectional transport and photon storage in an one-dimensional lattice with complex hopping rates
• Robust quantum boomerang effect in non-Hermitian systems
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems
• Optimal Fluctuations and Tail States of non-Hermitian Operators
• Phase transitions in non-Hermitian superlattices
• Optimal Fluctuations and Tail States of non-Hermitian Operators
• Asymptotically exact probability distribution for the Sinai model with finite drift
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields