Non-Hermitian propagation of Hagedorn wavepackets

TL;DR

This paper explores the non-Hermitian evolution of Hagedorn wavepackets, revealing new phenomena such as activation of excited states and establishing links between coherent states and Lagrangian frames.

Contribution

It introduces a novel polynomial recursion for non-Hermitian propagation and demonstrates its application to the Davies--Swanson oscillator, highlighting differences from Hermitian cases.

Findings

Activation of lower excited states during non-Hermitian evolution

Connection between coherent states and Lagrangian frames

Application to Davies--Swanson oscillator

Abstract

We investigate the time evolution of Hagedorn wavepackets by non-Hermitian quadratic Hamiltonians. We state a direct connection between coherent states and Lagrangian frames. For the time evolution a multivariate polynomial recursion is derived that describes the activation of lower lying excited states, a phenomenon unprecedented for Hermitian propagation. Finally we apply the propagation of excited states to the Davies--Swanson oscillator.