Spectral theory of non-Markovian dissipative phase transitions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914988106448896 |
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| author | Debecker, Baptiste Martin, John Damanet, François |
| author_facet | Debecker, Baptiste Martin, John Damanet, François |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral theory of non-Markovian dissipative phase transitions Debecker, Baptiste Martin, John Damanet, François Quantum Physics Statistical Mechanics 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. |
| title | Spectral theory of non-Markovian dissipative phase transitions |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2410.18990 |