Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians

TL;DR

This paper introduces a method to derive exact solutions for time-dependent Hermitian quantum systems using solutions from static non-Hermitian systems and the Dyson relation, demonstrated on a Rabi-type model.

Contribution

It presents a novel analytical approach connecting time-dependent Hermitian and static non-Hermitian Hamiltonians via the Dyson relation.

Findings

Successfully applied to a Hermitian Rabi-type model

Relates Hermitian dynamics to non-Hermitian lattice models

Provides exact solutions for time-dependent quantum systems

Abstract

We propose a procedure to obtain exact analytical solutions to the time-dependent Schr\"{o}dinger equations involving explicit time-dependent Hermitian Hamitonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.