Sharp inequalities for coherent states and their optimizers-Reference-Cited by-同舟云学术

Sharp inequalities for coherent states and their optimizers

Published:2023-01-01 Issue:1 Volume:23 Page:
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Frank Rupert L.¹²³

Affiliation:

1. Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39 , 80333 München , Germany

2. Munich Center for Quantum Science and Technology, Schellingstr. 4 , 80799 München , Germany

3. Mathematics 253-37, Caltech , Pasadena , CA 91125 , USA

Abstract

Abstract We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group, Lieb and Solovej for SU(2), and Kulikov for SU(1, 1) and the affine group. In this article, we give alternative proofs and characterize, for the first time, the optimizers in the general case. We also extend the recent Faber-Krahn-type inequality for Heisenberg coherent states, due to Nicola and Tilli, to the SU(2) and SU(1, 1) cases. Finally, we prove a family of reverse Hölder inequalities for polynomials, conjectured by Bodmann.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0050/pdf

Reference44 articles.

1. A. Alvino, G. Trombetti, and P.-L. Lions, On optimization problems with prescribed rearrangements, Nonlinear Anal. 13 (1989), no. 2, 185–220.

2. E. W. Aslaksen and J. R. Klauder, Unitary representations of the affine group, J. Mathematical Phys. 9 (1968), 206–211.

3. J. Bandyopadhyay, Optimal concentration for SU(1, 1) coherent state transforms and an analog of the Lieb-Wehrl conjecture for SU(1, 1), Comm. Math. Phys. 285 (2009), no. 3, 1065–1086.

4. J. L. Barbosa, M. doCarmo, and J. Eschenburg, Stability of hypersurfaces of constant mean curvature in Riemannian manifolds. Math. Z. 197 (1988), no. 1, 123–138.

5. V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. Math. 48 (1947), no. 2, 568–640.