Emulating non-Hermitian dynamics in a finite non-dissipative quantum system
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Flament, Eloi Impens, François Guéry-Odelin, David |
| author_facet | Flament, Eloi Impens, François Guéry-Odelin, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emulating non-Hermitian dynamics in a finite non-dissipative quantum system Flament, Eloi Impens, François Guéry-Odelin, David Quantum Physics 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. |
| title | Emulating non-Hermitian dynamics in a finite non-dissipative quantum system |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.02507 |