Exact solutions for time-dependent non-Hermitian oscillators: classical and quantum pictures

• URL: http://arxiv.org/abs/2108.08958v1
• Date: Fri, 20 Aug 2021 01:09:59 GMT
• Title: Exact solutions for time-dependent non-Hermitian oscillators: classical and quantum pictures
• Authors: Kevin Zelaya and Oscar Rosas-Ortiz
• Abstract summary: We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian configuration for the appropriate values of the involved parameters.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola-Kanai model as a particular case. Explicit solutions are given in both, the classical and quantum pictures.

Related papers

• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling [22.20907440445493]
  We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) This formulation does not depend on the discretization of the Schr"odinger equation and recurrence relations of special functions. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator.
  arXiv  Detail & Related papers  (2023-04-04T03:02:03Z)
• Quadratic Time-dependent Quantum Harmonic Oscillator [0.0]
  We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators. Our unitary-transformation-based approach provides a solution to our general quadratic time-dependent quantum harmonic model.
  arXiv  Detail & Related papers  (2022-11-23T19:50:49Z)
• Exact solution for the time dependent non-Hermitian generalized Swanson oscillator [0.0]
  A non-Hermitian setup characterized by time dependent complex coefficients is studied. The exact solution is obtained by applying two transformations and under the right choice of the relevant parameters.
  arXiv  Detail & Related papers  (2022-05-11T19:18:26Z)
• Nonlinear Classical and Quantum Integrable Systems with PT-symmetries [0.0]
  Key feature of integrable systems is that they can be solved to obtain exact analytical solutions. We show how new models can be constructed through generalisations of some well known nonlinear partial differential equations with PT-symmetries. We develop new methods from well-known ones to obtain exact analytical soliton solutions for these new systems.
  arXiv  Detail & Related papers  (2022-01-01T01:50:53Z)
• Intrinsic decoherence for the displaced harmonic oscillator [77.34726150561087]
  We use the complete solution of the Milburn equation that describes intrinsic decoherence. We calculate the expectation values of position quadrature, and the number operator in initial coherent and squeezed states.
  arXiv  Detail & Related papers  (2021-12-06T03:15:43Z)
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous [62.997667081978825]
  The impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom. The dynamics of this system is determined in closed analytical form. We observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior.
  arXiv  Detail & Related papers  (2021-11-23T20:25:57Z)
• Time and Evolution in Quantum and Classical Cosmology [68.8204255655161]
  We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.
  arXiv  Detail & Related papers  (2021-07-02T09:17:55Z)
• 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)
• Quantum limit-cycles and the Rayleigh and van der Pol oscillators [0.0]
  Self-oscillating systems are emerging as canonical models for driven dissipative nonequilibrium open quantum systems. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature.
  arXiv  Detail & Related papers  (2020-11-05T08:51:51Z)
• Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space [0.32771631221674324]
  We have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation.
  arXiv  Detail & Related papers  (2020-06-15T08:30:25Z)

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.