Continuum of Bound States in a Non-Hermitian Model
- URL: http://arxiv.org/abs/2210.03738v2
- Date: Sun, 8 Jan 2023 02:07:34 GMT
- Title: Continuum of Bound States in a Non-Hermitian Model
- Authors: Qiang Wang, Changyan Zhu, Xu Zheng, Haoran Xue, Baile Zhang and Y. D.
Chong
- Abstract summary: In a Hermitian system, bound states must have quantized energies, whereas extended states can form a continuum.
We show how this principle fails for non-Hermitian continuous Hamiltonians with an imaginary momentum and Landau-type vector potential.
We present experimentally-realizable 1D and 2D lattice models that can be used to study CLMs.
- Score: 6.229083355999047
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In a Hermitian system, bound states must have quantized energies, whereas
extended states can form a continuum. We demonstrate how this principle fails
for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians
with an imaginary momentum and Landau-type vector potential. The eigenstates,
which we call ``continuum Landau modes'' (CLMs), have gaussian spatial
envelopes and form a continuum filling the complex energy plane. We present
experimentally-realizable 1D and 2D lattice models that can be used to study
CLMs; the lattice eigenstates are localized and have other features that are
the same as in the continuous model. One of these lattices can serve as a
rainbow trap, whereby the response to an excitation is concentrated at a
position proportional to the frequency. Another lattice can act a wave funnel,
concentrating an input excitation onto a boundary over a wide frequency
bandwidth. Unlike recent funneling schemes based on the non-Hermitian skin
effect, this requires only a simple lattice design without nonreciprocal
couplings.
Related papers
- Edge state behavior of interacting Bosons in a Su-Schrieffer-Heeger lattice [0.9553307596675152]
We develop an effective Hamiltonian to model ultra cold interacting Bosons on an SSH like lattice.
To pinpoint the boundary states, we have developed an algorithm by generalizing the imaginary time propagator.
We draw a parallel to an experimentally physical setup involving a gas of ultra cold Bosons confined to an array of potential wells with alternating depths.
arXiv Detail & Related papers (2024-10-24T04:55:05Z) - A non-hermitean momentum operator for the particle in a box [49.1574468325115]
We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example.
The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
arXiv Detail & Related papers (2024-03-20T12:51:58Z) - Spontaneous formation of persistent square pattern in a driven
superfluid [0.6141800972050401]
We report on the spontaneous formation of square lattice patterns in a rotationally symmetric and driven Bose-Einstein condensate.
We show theoretically that this state can be understood as an attractive fixed point of coupled nonlinear amplitude equations.
arXiv Detail & Related papers (2023-09-07T15:43:18Z) - Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Fermion production at the boundary of an expanding universe: a cold-atom
gravitational analogue [68.8204255655161]
We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime.
We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
arXiv Detail & Related papers (2022-12-02T18:28:23Z) - 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) - Non-Hermitian skin effect beyond the tight-binding models [0.0]
The energy spectrum describes rather generally closed loops in complex plane, characterized by integer nonzero winding numbers.
We show that the NHSE is ubiquitous under OBC and characterized by a non-vanishing integer winding number.
We also show that the interior of the energy spectrum corresponds to the complex eigenenergies sustaining localized (edge) states under semi-infinite boundary conditions.
arXiv Detail & Related papers (2021-09-03T06:03:09Z) - 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) - Non-equilibrium stationary states of quantum non-Hermitian lattice
models [68.8204255655161]
We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner.
We focus on the quantum steady states of such models for both fermionic and bosonic systems.
arXiv Detail & Related papers (2021-03-02T18:56:44Z) - Quantum anomalous Hall phase in synthetic bilayers via twistless
twistronics [58.720142291102135]
We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions.
We show that our system exhibits topologicalband structures under appropriate conditions.
arXiv Detail & Related papers (2020-08-06T19:58:05Z)
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.