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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2512.23414 |
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| _version_ | 1866909977678970880 |
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| author | Li, Zheng |
| author_facet | Li, Zheng |
| contents | In arXiv:2405.04947, it was shown that the GNS spectral gap of a Gaussian quantum Markovian generator is strictly positive if and only if there exists a maximal number of linearly independent noise operators, under the assumption that the generated semigroup admits a unique faithful normal invariant state. In this paper, we provide a necessary and sufficient condition for the existence of the KMS spectral gap, which also depends only on the noise operators of the generator. We further show that the existence of the GNS spectral gap implies the existence of the KMS spectral gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of the KMS spectral gap in Gaussian quantum Markov semigroups Li, Zheng Functional Analysis Quantum Physics 46L53, 46L55, 81S22 In arXiv:2405.04947, it was shown that the GNS spectral gap of a Gaussian quantum Markovian generator is strictly positive if and only if there exists a maximal number of linearly independent noise operators, under the assumption that the generated semigroup admits a unique faithful normal invariant state. In this paper, we provide a necessary and sufficient condition for the existence of the KMS spectral gap, which also depends only on the noise operators of the generator. We further show that the existence of the GNS spectral gap implies the existence of the KMS spectral gap. |
| title | On the existence of the KMS spectral gap in Gaussian quantum Markov semigroups |
| topic | Functional Analysis Quantum Physics 46L53, 46L55, 81S22 |
| url | https://arxiv.org/abs/2512.23414 |