Emulating non-Hermitian dynamics in a finite non-dissipative quantum system

• URL: http://arxiv.org/abs/2502.02507v1
• Date: Tue, 04 Feb 2025 17:24:07 GMT
• Title: Emulating non-Hermitian dynamics in a finite non-dissipative quantum system
• Authors: Eloi Flament, François Impens, David Guéry-Odelin,
• Abstract summary: We discuss the emulation of non-Hermitian dynamics during a given time window. We use a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We show that such a continuum can reproduce non-Hermitian dynamics more efficiently than the usual quasi-continuum model.
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• Abstract: We discuss the emulation of non-Hermitian dynamics during a given time window by a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an unstable state, and map the quasi-continuum parameters enabling a precise approximation of the non-Hermitian dynamics. The limitations of this model, including in particular short- and long- time deviations, are extensively discussed. We then consider a driven two-dimensional system, and establish criteria for the non-Hermitian dynamics emulation with a finite quasi-continuum. We quantitatively analyze the signatures of finiteness of the effective continuum, addressing the possible emergence of non-Markovian behavior during the time interval considered. Finally, we investigate the emulation of dissipative dynamics using a finite quasi-continuum with a tailored density of states. We show on the example of a two-level system that such a continuum can reproduce non-Hermitian dynamics more efficiently than the usual equidistant quasi-continuum model.

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