发表机构
Tsinghua University; Beijing Institute of Mathematical Sciences and Applications（清华大学; 北京国际数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为本原KMS对称量子马尔可夫半群建立了量子Cheeger不等式，并证明了其超压缩性和对数Sobolev不等式，且应用于完全修正对数Sobolev不等式。
AI 中文摘要
本文针对本原KMS对称量子马尔可夫半群，建立了基于投影电导的量子Cheeger不等式。我们讨论了基于图的KMS对称量子马尔可夫半群的投影电导和经典电导。我们证明了本原KMS对称量子马尔可夫半群满足超压缩性和对数Sobolev不等式。我们还展示了量子Cheeger不等式在对数Sobolev不等式、超压缩性和完全修正对数Sobolev不等式中的应用。
英文摘要
In this paper, we establish a quantum Cheeger inequality for primitive KMS-symmetric quantum Markov semigroups in terms of projection conductance. We discuss both projection conductance and classical conductance for graph-based KMS-symmetric quantum Markov semigroups. We show that hypercontractivity and the logarithmic Sobolev inequality hold for primitive KMS-symmetric quantum Markov semigroups. We also present applications of the quantum Cheeger inequality to logarithmic Sobolev inequalities, hypercontractivity, and complete modified logarithmic Sobolev inequalities.
