The Wehrl-type entropy conjecture for symmetric $SU(N)$ coherent states: cases of equality and stability
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| Format: | Preprint |
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2024
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| _version_ | 1866911218668666880 |
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| author | Nicola, Fabio Riccardi, Federico Tilli, Paolo |
| author_facet | Nicola, Fabio Riccardi, Federico Tilli, Paolo |
| contents | Lieb and Solovej proved that, for the symmetric $SU(N)$ representations, the corresponding Wehrl-type entropy is minimized by symmetric coherent states. However, the uniqueness of the minimizers remained an open problem when $N\geq 3$. In this note, we complete the proof of the Wehrl entropy conjecture for such representations by showing that symmetric coherent states are, in fact, the only minimizers. We also provide an application to the maximum concentration of holomorphic polynomials and deduce a corresponding Faber-Krahn inequality. A sharp quantitative form of the bound by Lieb and Solovej is also proved. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Wehrl-type entropy conjecture for symmetric $SU(N)$ coherent states: cases of equality and stability Nicola, Fabio Riccardi, Federico Tilli, Paolo Mathematical Physics Functional Analysis Quantum Physics Lieb and Solovej proved that, for the symmetric $SU(N)$ representations, the corresponding Wehrl-type entropy is minimized by symmetric coherent states. However, the uniqueness of the minimizers remained an open problem when $N\geq 3$. In this note, we complete the proof of the Wehrl entropy conjecture for such representations by showing that symmetric coherent states are, in fact, the only minimizers. We also provide an application to the maximum concentration of holomorphic polynomials and deduce a corresponding Faber-Krahn inequality. A sharp quantitative form of the bound by Lieb and Solovej is also proved. |
| title | The Wehrl-type entropy conjecture for symmetric $SU(N)$ coherent states: cases of equality and stability |
| topic | Mathematical Physics Functional Analysis Quantum Physics |
| url | https://arxiv.org/abs/2412.10940 |