Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{PT}$-symmetric non-Hermitian systems

• URL: http://arxiv.org/abs/2007.04591v1
• Date: Thu, 9 Jul 2020 07:02:49 GMT
• Title: Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{PT}$-symmetric non-Hermitian systems
• Authors: Chon-Fai Kam and Yang Chen
• Abstract summary: The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. We identify different transmission dynamics separated by exceptional points, and derive analytical approximate formulas for the non-adiabatic transmission probabilities. We discuss possible experimental realizations with a $mathcalPmathcalT$-symmetric non-Hermitian one-dimensional tight-binding optical waveguide lattice.
• Score: 4.4074213830420055
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formulas for the non-adiabatic transmission probabilities. We discuss possible experimental realizations with a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian one-dimensional tight-binding optical waveguide lattice.

Related papers

• 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)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model [44.58985907089892]
  How the property of quantum many-body system especially the phase transition will be affected by the non-hermiticity remains unclear. We show that there is a continuous phase transition induced by the non-hermiticity in QCP. We observe that the order parameter and susceptibility display infinitely even for finite size system, since non-hermiticity endows universality many-body system with different singular behaviour from classical phase transition.
  arXiv  Detail & Related papers  (2022-09-22T01:11:28Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{PT}$ symmetry [15.273168396747495]
  Non-Hermitian systems with parity-time reversal ($mathcalPT$) or anti-$mathcalPT$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. We implement a Floquet Hamiltonian of a single qubit with anti-$mathcalPT$ symmetry by periodically driving a dissipative quantum system of a single trapped ion.
  arXiv  Detail & Related papers  (2021-07-27T07:11:32Z)
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{PT}\!-$symmetric systems [0.0]
  Non-Hermitian systems with parity-time ($mathcalPT$) symmetry and anti-$mathcalPT$ symmetry give rise to exceptional points (EPs) We propose a powerful and easily computable tool, based on the Hilbert-Schmidt speed (HSS), which does not require the diagonalization of the evolved density matrix. We find that the trace distance, a measure of distinguishability of two arbitrary quantum states, may be non-contractive under the non-Hermitian evolution of the system.
  arXiv  Detail & Related papers  (2021-01-12T18:42:52Z)
• Stable States with Non-Zero Entropy under Broken $\mathcal{PT}$-Symmetry [1.3049516752695611]
  We focus on the dynamical features of a triple-qubit system, one of which evolves under local $mathcalPT$-symmetric Hamiltonian. A new kind of abnormal dynamic pattern in the entropy evolution process is identified, which presents a parameter-dependent stable state. Our work reveals the distinctive dynamic features in the triple-qubit $mathcalPT$-symmetric system and paves the way for practical quantum simulation of multi-party non-Hermitian system on quantum computers.
  arXiv  Detail & Related papers  (2021-01-01T05:56:28Z)
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder [0.0]
  Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical and transport properties. We introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.
  arXiv  Detail & Related papers  (2020-06-16T03:22:53Z)
• Observation of Hermitian and Non-Hermitian Diabolic Points and Exceptional Rings in Parity-Time symmetric ZRC and RLC Dimers [62.997667081978825]
  We show how appears non-Hermitian degeneracy points in the spectrum and how they are protected against a Hermitian perturbation. This work opens a gold road for investigations on topological electrical circuits for robust transport of information at room temperature.
  arXiv  Detail & Related papers  (2020-04-17T15:51:49Z)
• On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms [0.0]
  The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential.
  arXiv  Detail & Related papers  (2020-01-09T00:42:22Z)

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.