Time evolution of quantum systems with time-dependent non-Hermitian Hamiltonian and the pseudo Hermitian invariant operator

TL;DR

This paper investigates the dynamics of quantum systems governed by time-dependent non-Hermitian Hamiltonians combining SU(1,1) and SU(2) symmetries, constructing a pseudo-Hermitian invariant operator to find exact solutions.

Contribution

It introduces a method to construct a pseudo-Hermitian invariant operator for such systems and derives exact solutions of the Schrödinger equation.

Findings

Exact solutions for SU(1,1) and SU(2) systems obtained

Pseudo-Hermitian invariant operator constructed with a time-dependent metric

Unified approach to time evolution in non-Hermitian quantum systems

Abstract

We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. The exact common solutions of the Schr\"odinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the pseudo-Hermitian invariant operator.