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arXiv · 2410.18990

Spectral theory of non-Markovian dissipative phase transitions

Baptiste Debecker·John Martin·François Damanet
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Abstract

Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the spectral theory of dissipative phase transitions to non-Markovian systems, encompassing a much broader class of quantum materials and experiments and opening many possibilities for non-Markovian engineering of matter phases such as, as explored in the companion Letter [Debecker et. al., Phys. Rev. Lett. 133, 140403 (2024)], reshaping of phase boundaries and triggering of phase transitions. We first prove several statements about the connections between the spectrum of the generator of the non-Markovian dynamics of general systems and dissipative phase transitions. Then, as a benchmark, we show that our framework can capture all the expected signatures of the superradiant phase transition appearing in a challenging $U(1)$-symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.

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Baptiste Debecker, John Martin, François Damanet. 2024-10-10. Spectral theory of non-Markovian dissipative phase transitions. https://doi.org/10.1103/physreva.110.042201

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