Three perspectives on entropy dynamics in a non-Hermitian two-state system
- URL: http://arxiv.org/abs/2404.03492v1
- Date: Thu, 4 Apr 2024 14:45:28 GMT
- Title: Three perspectives on entropy dynamics in a non-Hermitian two-state system
- Authors: Alexander Felski, Alireza Beygi, Christos Karapoulitidis, S. P. Klevansky,
- Abstract summary: entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented.
We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
- Score: 41.94295877935867
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken $\mathcal{PT}$ symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its $\mathcal{PT}$-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the $\mathcal{PT}$ charge operator $\mathcal{C}$. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry.
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