Spontaneous symmetry breaking for nonautonomous pseudo-Hermitian systems
Abstract
Here we first present an alternative formulation of the Lewis & Riesenfeld theorem for solving the Schr\"odinger equation with nonautonomous Hermitian and pseudo-Hermitian Hamiltonians. We then employ this framework to characterize the spontaneous breaking of time-dependent antilinear symmetries of these Hamiltonians. We demonstrate that, under unbroken antilinear symmetries, the Lewis & Riesenfeld phases are real and odd functions of time, which allows us to recover the well-known real spectra of time-independent pseudo-Hermitian Hamiltonians. However, in the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise, leading to coalescence effects analogous to those in the time-independent scenario. Finally, we present an illustrative example of unbroken and broken PT-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect.
Keywords
Cite
@article{arxiv.2504.02050,
title = {Spontaneous symmetry breaking for nonautonomous pseudo-Hermitian systems},
author = {L. F. Alves da Silva and M. H. Y. Moussa},
journal= {arXiv preprint arXiv:2504.02050},
year = {2026}
}