Time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics

TL;DR

This paper investigates how quantum systems with $PT$-symmetry evolve over time and under adiabatic conditions, providing equations and criteria specific to such Hamiltonians.

Contribution

It introduces the time evolution equation and adiabatic approximation conditions tailored for $PT$-symmetric quantum Hamiltonians.

Findings

Derived the time evolution equation for $PT$-symmetric Hamiltonians

Established conditions for the validity of adiabatic approximation in $PT$-symmetric systems

Provided theoretical framework for analyzing $PT$-symmetric quantum dynamics

Abstract

In this paper, we discuss time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics. we give the time evolving equation for a class of $PT$-symmetric Hamiltonians and some conditions of the adiabatic approximation for the class of $PT$-symmetric Hamiltonians.