Adiabatic time-dependent metrics in PT-symmetric quantum theories

TL;DR

This paper develops a method for analyzing scattering in PT-symmetric quantum theories using adiabatic switching of interactions and explores the conditions for the validity of time-dependent metrics.

Contribution

It introduces an approach to handle scattering in PT-symmetric theories with time-dependent metrics and establishes an adiabatic theorem analogue for these metrics.

Findings

Adiabatic switching can be used in PT-symmetric scattering problems.

Time-dependent metrics require specific modifications to standard methods.

An adiabatic theorem analogue is valid for these metrics, ensuring consistency.

Abstract

We introduce an approach to scattering problems in theories with non-Hermitian Hamiltonian, usually known as PT-symmetric quantum theories, by means of the adiabatic switching of the interaction. The modifications of usual methods needed to employ time-dependent metrics are described. We argue that an analogue of the adiabatic theorem hold for time dependent metrics and that its validity forms a necessary condition for consistency of the procedure.