Exactly solvable time-dependent non-Hermitian quantum systems from point transformations

• URL: http://arxiv.org/abs/2105.01486v1
• Date: Tue, 4 May 2021 13:24:23 GMT
• Title: Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Authors: Andreas Fring and Rebecca Tenney
• Abstract summary: We construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. We obtain solutions to the time-dependent Dyson and time-dependent quasi-Hermiticity equation together with solutions to the corresponding time-dependent Schr"odinger equation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. Initially we identify a point transformation as a map from an exactly solvable time-independent system to an explicitly time-dependent non-Hermitian Hamiltonian system. Subsequently we employ the point transformation to construct the non-Hermitian time-dependent invariant for the latter system. Exploiting the fact that this invariant is pseudo-Hermitian, we construct a corresponding Dyson map as the adjoint action from a non-Hermitian to a Hermitian invariant, thus obtaining solutions to the time-dependent Dyson and time-dependent quasi-Hermiticity equation together with solutions to the corresponding time-dependent Schr\"odinger equation.

Related papers

• Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation [33.76659022113328]
  This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension.
  arXiv  Detail & Related papers  (2024-07-22T03:52:14Z)
• Nonlinear dynamics as a ground-state solution on quantum computers [39.58317527488534]
  We present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation.
  arXiv  Detail & Related papers  (2024-03-25T14:06:18Z)
• Non-Hermitian Quantum Fermi Accelerator [0.0]
  We solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways.
  arXiv  Detail & Related papers  (2023-04-17T02:29:12Z)
• 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)
• Unitary evolution for a two-level quantum system in fractional-time scenario [0.0]
  We show that it is possible to map the non-unitary time-evolution operator in a unitary one. We consider three examples of Hamiltonian operators and their corresponding unitary dynamics.
  arXiv  Detail & Related papers  (2022-08-29T19:57:30Z)
• Entanglement between uncoupled modes with time-dependent complex frequency [0.0]
  We present the general unified description for the unitary time-evolution generated by time-dependent non-Hermitian Hamiltonians. As a direct consequence, we verify that a time-evolved state of uncoupled modes by a time-dependent complex frequency may exhibits a non-zero entanglement.
  arXiv  Detail & Related papers  (2022-06-28T17:00:28Z)
• Exact solutions for time-dependent complex symmetric potential well [0.0]
  We investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well. The problem is exactly solvable and the analytic expressions of the Schr"odinger wavefunctions are given in terms of the Airy function.
  arXiv  Detail & Related papers  (2022-06-09T16:18:02Z)
• On Statistical Distribution for Adiabatically Isolated Body [62.997667081978825]
  The statistical distribution for the case of an adiabatically isolated body was obtained in the framework of covariant quantum theory. The energy of an isolated system is an external parameter for the modified distribution instead of temperature.
  arXiv  Detail & Related papers  (2022-05-15T09:33:36Z)
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems [0.0]
  I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric. I will explain how generalised versions of this antilinear symmetry can be utilised to explain that these type of systems possess real eigenvalue spectra in parts of their parameter spaces. I will explain how to extend this framework to explicitly time-dependent Hamiltonian systems.
  arXiv  Detail & Related papers  (2022-01-13T18:52:30Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
  We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We modify the time-dependent Schr"odinger equation through a change of representation. The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
  arXiv  Detail & Related papers  (2020-11-23T17:29:31Z)

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.