紧致连通半单李群的Wehrl型熵问题
Wehrl-type entropy problem for compact connected semisimple Lie groups
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中文总结 AI 辅助
本文通过二阶变分法证明紧致连通半单李群中相干投影子唯一极小化Wehrl熵并最大化Husimi幂矩，将问题归结为最高权向量的极矩性质。
中文摘要 AI 辅助
本文解决了任意紧致连通半单李群的Wehrl型熵问题。设$G$为紧致连通半单李群，$\u03c0:G\u2192U(V_\u03bb)$为与最高权$\u03bb$相关的有限维不可约酉表示。我们证明相干投影子是$V_\u03bb$上所有密度矩阵中Wehrl熵的唯一极小化子。它们也唯一地最大化每个阶$p>1$的Husimi幂矩。证明使用在极值点处沿与Killing场相关的方向进行扰动的二阶变分，类似于Frank和Lieb在\cite{FrankLieb}中使用的策略。然后问题归结为最高权向量的极矩性质。
英文摘要
This paper solves the Wehrl-type entropy problem for arbitrary compact connected semisimple Lie groups. Let $G$ be a compact connected semisimple Lie group, and let $π:G\to U(V_λ)$ be a finite-dimensional irreducible unitary representation associated with the highest weight $λ$. We prove that coherent projectors are the unique minimizers of the Wehrl entropy over all density matrices on $V_λ$. They also uniquely maximize every Husimi power moment of order $p>1$. The proof uses a second-variation at the extremizer by perturbation in directions associated with Killing fields, similar to the strategy of Frank and Lieb used in \cite{FrankLieb}. Then the problem reduces to the extreme-moment property of highest-weight vectors.
发表机构
- University of South Carolina（南卡罗来纳大学）
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