Spontaneous symmetry breaking for nonautonomous Hermitian or non-Hermitian systems

• URL: http://arxiv.org/abs/2504.02050v1
• Date: Wed, 02 Apr 2025 18:13:48 GMT
• Title: Spontaneous symmetry breaking for nonautonomous Hermitian or non-Hermitian systems
• Authors: L. F. Alves da Silva, M. H. Y. Moussa,
• Abstract summary: We show that if the general antilinear symmetry is unbroken, the Lewis & Riesenfeld phases are real odd functions of time.<n>For the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise as even functions of time.<n>We present an illustrative example of the unbroken and broken $mathcalPT$-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Here we first present an alternative approach to the Lewis & Riesenfeld theorem for solving the Schr\"odinger equation for time-dependent Hermitian or pseudo-Hermitian Hamiltonians. Then, we apply this framework to the problem of spontaneous breaking of time-dependent antilinear symmetries associated with those Hamiltonians. We demonstrate that if the general antilinear symmetry is unbroken, the Lewis & Riesenfeld phases are real odd functions of time, which allows up to recover the real spectra of time-independent pseudo-Hermitian Hamiltonians. For the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise as even functions of time, resulting in the coalescence of the real eigenvalues of the unbroken regime. We present an illustrative example of the unbroken and broken $\mathcal{PT}$-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect.

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