Non-hermitian time evolution: from static to parametric instability
Abstract
Eigenmode coalescence imparts remarkable properties to non-hermitian time evolution, culminating in a purely non-hermitian spectral degeneracy known as an exceptional point (EP). Here, we revisit time evolution at the EP and classify two-level non-hermitian Hamiltonians in terms of the M\"obius group. We then leverage that classification to study dynamical EP encircling, by applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that Floquet non-hermitian systems exhibit rich physics whose complexity is not captured by an EP-encircling rule. For example, Floquet EPs can occur without encircling and vice-versa. Instead, we show that the elaborate interplay between non-hermitian and modulation instabilities is better understood through the lens of parametric resonance.
Cite
@article{arxiv.2103.15915,
title = {Non-hermitian time evolution: from static to parametric instability},
author = {Aleksi Bossart and Romain Fleury},
journal= {arXiv preprint arXiv:2103.15915},
year = {2021}
}