Year: 2026
Type: preprint
Abstract: 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 $V_λ$. Similar extremal properties hold for power functions in place of the entropy function. 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 uncertainty principle characterizing coherent states. This solves the Wehrl-type entropy problem for arbitrary compact connected semisimple Lie groups.
Source: arXiv (Cornell University)
Author: Zhang, Haonan
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213510777