Wave packet evolution in non-Hermitian quantum systems

TL;DR

This paper explores how Gaussian wave packets evolve in non-Hermitian quantum systems, revealing a complex phase space structure and a non-Hermitian analog of Ehrenfest's theorem in the semiclassical limit.

Contribution

It introduces a framework for understanding wave packet dynamics in non-Hermitian systems, highlighting the role of complex phase space and metric evolution.

Findings

Derivation of non-Hermitian Ehrenfest theorem for expectation values

Identification of coupled equations for phase space and metric

Demonstration of complex structure's impact on quantum dynamics

Abstract

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase space metric---a phenomenon having no analog in Hermitian theories.