PreprintCC BY-NC-ND 4.0arXiv
Wehrl-type entropy problem for compact connected semisimple Lie groups
Abstract
Let G be a compact connected semisimple Lie group, and let π:G→ U(Vλ) 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 Vλ. 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.
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BibTeX
@misc{zhang2026wehrltype,
title = {{Wehrl-type entropy problem for compact connected semisimple Lie groups}},
author = {Haonan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.18919},
eprint = {2609.18919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18919},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Wehrl-type entropy problem for compact connected semisimple Lie groups
AU - Haonan Zhang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.18919
UR - https://arxiv.org/abs/2609.18919
AB - Let G be a compact connected semisimple Lie group, and let π:G→ 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.
ER -