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arXiv · 2406.17436

Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation

Takano Taira·Naomichi Hatano·Akinori Nishino
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Abstract

The dynamics of a two-level system coupled to a particle bath with the Dirac dispersion relation is studied. We analytically show that closing the Dirac gap results in a transition of the survival probability of the two-level system from non-exponential to exponential decay in the long-time regime, while the short-time regime remains exponential. The exact time-evolving state is also calculated. With the Dirac gap closing smoothly, the time-evolving state converges to a time-evolving resonant state, which is normalizable due to causality. We numerically show that introducing a finite cutoff to the Dirac dispersion relation leads to a transition from exponential to non-exponential decay both in short- and long-time regimes, with the time-evolving resonant state resolved to a time-evolving state. Furthermore, we propose several experimental setups that act as a particle bath with the Dirac dispersion relation. We give a detailed calculation for one of them, namely an optical array in the Su-Schrieffer-Heeger configuration. In this case, we show that our theoretical results can be observed experimentally with realistic parameters in an existing experimental setup of an optical waveguide array.

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Takano Taira, Naomichi Hatano, Akinori Nishino. 2024-06-25. Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation. https://arxiv.org/abs/2406.17436

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