On the existence of the KMS spectral gap in Gaussian quantum Markov semigroups

• URL: http://arxiv.org/abs/2512.23414v1
• Date: Mon, 29 Dec 2025 12:18:36 GMT
• Title: On the existence of the KMS spectral gap in Gaussian quantum Markov semigroups
• Authors: Zheng Li,
• Abstract summary: 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.<n>We show that the existence of the GNS spectral gap implies the existence of the KMS spectral gap.
• Score: 5.339049926920038
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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