Nonadiabatic transitions in non-Hermitian $\mathcal{PT}$-symmetric two-level systems

• URL: http://arxiv.org/abs/2301.10382v2
• Date: Wed, 15 Nov 2023 02:43:08 GMT
• Title: Nonadiabatic transitions in non-Hermitian $\mathcal{PT}$-symmetric two-level systems
• Authors: Jian-Song Pan and Fan Wu
• Abstract summary: We systematically characterize the evolution of time-parity systems with spin-dependent dissipations. We find that the behaviors of particle probability on the two levels show initial-state-independent redistribution in the slow-speed limit. The predicted equal-distribution phenomenon may be employed to identify gap closing from anti-crossing between two energy bands.
• Score: 3.7440572759222692
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We systematically characterize the dynamical evolution of time-parity ($\mathcal{PT}$)-symmetric two-level systems with spin-dependent dissipations. When the energy-gap control parameters are tuned, a section of imaginary spectra ended with exceptional points (EP) appears in the regimes where the dissipation term is dominant. If the parameters are linearly tuned with time, the dynamical evolution can be characterized with the parabolic cylinder equations, which can be analytically solved. We find that the asymptotic behaviors of particle probability on the two levels show initial-state-independent redistribution in the slow-tuning-speed limit when the system is nonadiabatically driven across EPs. Equal distributions appear when the non-dissipative Hamiltonian shows gap closing. So long as the non-dissipative Hamiltonian displays level anti-crossing, the final distribution becomes unbalanced. The ratios between the occupation probabilities are given analytically. These results are confirmed with numerical simulations. The predicted equal-distribution phenomenon may be employed to identify gap closing from anti-crossing between two energy bands.

Related papers

• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Quantum many-body spin ratchets [0.0]
  We show that breaking of space-reflection symmetry results in a drift in the dynamical spin susceptibility. We also show that the scaled cumulant generating function of the time-integrated current instead obeys a generalized fluctuation relation.
  arXiv  Detail & Related papers  (2024-06-03T17:51:36Z)
• 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)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Spectral and steady-state properties of fermionic random quadratic Liouvillians [0.3774866290142281]
  We study spectral and steady-state properties of generic Markovian dissipative systems. We find two distinct phases where the support of the single-particle spectrum has one or two connected components.
  arXiv  Detail & Related papers  (2022-10-14T16:55:51Z)
• Clean two-dimensional Floquet time-crystal [68.8204255655161]
  We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. We observe a non-perturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.
  arXiv  Detail & Related papers  (2022-05-10T13:04:43Z)
• 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)
• False signals of chaos from quantum probes [0.0]
  We demonstrate that two-time correlation functions, which are generalizations of out-of-time-ordered correlators, can show 'false-flags' of chaos. We analyze a system of bosons trapped in a double-well potential and probed by a quantum dot.
  arXiv  Detail & Related papers  (2021-08-20T22:36:06Z)
• Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems [3.8654139025964875]
  We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors.
  arXiv  Detail & Related papers  (2020-07-06T18:00:01Z)
• Feedback-induced instabilities and dynamics in the Jaynes-Cummings model [62.997667081978825]
  We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system.
  arXiv  Detail & Related papers  (2020-06-20T10:07:01Z)
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase [0.0]
  We investigate the transition probabilities for the "flavor" eigenstates in the two-level quantum system. We show that the diverging behavior of the transition probabilities is actually applicable to the gauge-transformed neutral-meson states. We also present a brief review on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.
  arXiv  Detail & Related papers  (2020-02-13T14:04:04Z)

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.