Nonlinear non-Hermitian skin effect
- URL: http://arxiv.org/abs/2106.11748v1
- Date: Tue, 8 Jun 2021 11:32:22 GMT
- Title: Nonlinear non-Hermitian skin effect
- Authors: C. Yuce
- Abstract summary: Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues in a nonlocal way.
We show that fractal and continuum bands arise in a long lattice governed by a nonreciprocal discrete nonlinear Schrodinger equation.
We show that stationary solutions are localized at the edge in the continuum band.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Distant boundaries in linear non-Hermitian lattices can dramatically change
energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect
is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin
effect with nonlinear effects can give rise to a host of novel phenomenas,
which may be used for nonlinear structure designs. Here we study nonlinear
non-Hermitian skin effect and explore nonlocal and substantial effects of edges
on stationary nonlinear solutions. We show that fractal and continuum bands
arise in a long lattice governed by a nonreciprocal discrete nonlinear
Schrodinger equation. We show that stationary solutions are localized at the
edge in the continuum band. We consider a non-Hermitian Ablowitz-Ladik model
and show that nonlinear exceptional point disappears if the lattice is
infinitely long.
Related papers
- Nonlinear skin modes and fixed-points [0.0]
We investigate a one-dimensional tight-binding lattice with asymmetrical couplings and various type of nonlinearities to study nonlinear non-Hermitian skin effect.
We identify distinctive features of nonlinear skin modes, such as power-energy dependence, degeneracy, and power-energy discontinuity.
arXiv Detail & Related papers (2024-11-19T11:22:42Z) - Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.
These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.
We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
arXiv Detail & Related papers (2024-10-24T10:16:47Z) - Critical spin models from holographic disorder [49.1574468325115]
We study the behavior of XXZ spin chains with a quasiperiodic disorder not present in continuum holography.
Our results suggest the existence of a class of critical phases whose symmetries are derived from models of discrete holography.
arXiv Detail & Related papers (2024-09-25T18:00:02Z) - A class of stable nonlinear non-Hermitian skin modes [0.0]
The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems.
NHSE causes a large number of eigenstates to become localized at the boundary.
This paper introduces a method for achieving a stable localized state in a nonlinear finite lattice.
arXiv Detail & Related papers (2024-07-11T21:55:01Z) - Topological properties of a non-Hermitian quasi-1D chain with a flat
band [0.0]
spectral properties of a non-Hermitian quasi-1D lattice in two of the possible dimerization configurations are investigated.
Non-Hermitian diamond chain that presents a zero-energy flat band.
Non-Hermitian diamond chains can be mapped into two models of the Su-Schrieffer-Heeger chains, either non-Hermitian, and Hermitian, both in the presence of a flat band.
arXiv Detail & Related papers (2023-07-17T18:00:47Z) - Dynamical chaos in nonlinear Schr\"odinger models with subquadratic
power nonlinearity [137.6408511310322]
We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity.
We show that the spreading process is subdiffusive and has complex microscopic organization.
The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
arXiv Detail & Related papers (2023-01-20T16:45:36Z) - Anomalously large relaxation times in dissipative lattice models beyond
the non-Hermitian skin effect [49.1574468325115]
We show for generic quantum non-Hermitian tight-binding models that relaxation of local observables are not controlled by the localization length.
interference between eigenvectors effectively makes the extreme localization of modes largely irrelevant to relaxation.
Our work highlights an important aspect of the non-Hermitian skin effect: the exceptional sensitivity to boundary conditions here necessarily takes a finite amount of time to manifest itself.
arXiv Detail & Related papers (2022-10-25T17:55:58Z) - Non-Hermiticity induced Exceptional Points and Skin Effect in the
Dice-Haldane Model [12.632098351321218]
We investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice.
We introduce non-Hermiticity into this model in two ways -- through balanced non-Hermitian gain and loss, and by non-reciprocal hopping in one direction.
Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.
arXiv Detail & Related papers (2022-07-29T11:13:09Z) - Designing Kerr Interactions for Quantum Information Processing via
Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes.
Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation.
Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
arXiv Detail & Related papers (2021-07-14T15:11:05Z) - Long-lived period-doubled edge modes of interacting and disorder-free
Floquet spin chains [68.8204255655161]
We show that even in the absence of disorder, and in the presence of bulk heating, $pi$ edge modes are long lived.
A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace.
arXiv Detail & Related papers (2021-05-28T12:13:14Z) - Quasi-stationary solutions in non-Hermitian systems [0.0]
Eigenstates exhibit localization at an open edge in a non-Hermitian lattice due to non-Hermitian skin effect.
We predict quasi-stationary solutions, which are approximately time-independent.
arXiv Detail & Related papers (2021-03-23T17:25:04Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.