Dynamics of finite dimensional non-hermitian systems with indefinite metric

TL;DR

This paper explores the dynamics of finite-dimensional non-Hermitian quantum systems, employing Krein space theory to define inner products and analyzing dissipative Hamiltonians' stationary behavior and decoherence effects.

Contribution

It introduces a framework using Krein spaces for non-Hermitian systems and applies it to study dissipative Hamiltonians and their stationary states.

Findings

Krein space methods effectively define inner products for non-Hermitian systems.

Dissipative One Axis Twisting Hamiltonians exhibit specific stationary behaviors.

Decoherence impacts vary under different coupling schemes.

Abstract

We discuss the time evolution of physical finite dimensional systems which are modelled by non-hermitian Hamiltonians. We address both general non-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory of Krein Spaces to construct metric operators and well-defined inner products. As an application, we study the stationary behaviour of dissipative One Axis Twisting Hamiltonians. We discuss the effect of decoherence under different coupling schemes.