aqora

Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures

Kevin Zelaya, Óscar Rosas-Ortiz

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 spectra, 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.

arXiv:2108.08958Quantum ReportsAug 21, 202119 citations

Exact quantum-statistical dynamics of time-dependent generalized oscillators

Sang Pyo Kim, Don Nelson Page

arXiv:quant-ph/0205006Physics Letters BMay 7, 20134 citations

Non-Hermitian Swanson model with a time-dependent metric

Andreas Fring, M. H. Y. Moussa

We provide further nontrivial solutions to the recently proposed time-dependent Dyson and quasi-Hermiticity relation. Here, we solve them for the generalized version of the non-Hermitian Swanson Hamiltonian with time-dependent coefficients. We construct time-dependent solutions by employing the Lewis-Riesenfeld method of invariants and discuss concrete physical applications of our results.

arXiv:1606.04807Physical Review AOct 26, 201671 citations

The exact solution for the generalized time-dependent harmonic oscillator and its adiabatic limit

Xiao-Chun Gao, Jing-Bo Xu, Tiezheng Qian

Annals of PhysicsOct 1, 19902 citations

Energy evolution of a general one-dimensional oscillator with a quadratic time-dependent stiffness and a linear time-dependent correlation parameter

V. V. Dodonov, Alexandre V. Dodonov

We solve the time-dependent Schrödinger equation describing a generalized harmonic oscillator in the coordinate representation with constant mass but time-dependent stiffness and correlation parameters. Exact solutions are obtained in terms of confluent hypergeometric functions or parabolic cylinder functions. The dynamics of mean energy is studied in several different regimes, including the special case of imaginary correlation parameter, corresponding to the non-Hermitian Ahmed–Swanson model. In this case, real time-dependent mean values of the Hamiltonian are obtained by using dual wave functions, evolving according to the time-dependent Schrödinger equations with the given Hamiltonian and its Hermitially conjugated partner. The adiabatic evolution is considered as one of examples.We solve the time-dependent Schrödinger equation describing a generalized harmonic oscillator in the coordinate representation with constant mass but time-dependent stiffness and correlation parameters. Exact solutions are obtained in terms of confluent hypergeometric functions or parabolic cylinder functions. The dynamics of mean energy is studied in several different regimes, including the special case of imaginary correlation parameter, corresponding to the non-Hermitian Ahmed–Swanson model. In this case, real time-dependent mean values of the Hamiltonian are obtained by using dual wave functions, evolving according to the time-dependent Schrödinger equations with the given Hamiltonian and its Hermitially conjugated partner. The adiabatic evolution is considered as one of examples.

Journal of Mathematical PhysicsJan 1, 20251 citation

The exact solution for the generalized time-dependent harmonic oscillator and its adiabatic limit

Xiao-Chun Gao, Jing‐Bo Xu, Tiezheng Qian

Annals of PhysicsNov 1, 199079 citations

Exact solution for the time-dependent non-Hermitian generalized Swanson oscillator

Related papers

Exact solution for the time-dependent non-Hermitian generalized Swanson oscillator

Related papers