Selected Key Publications by Bernhard G . Bodmann

B. G. Bodmann (2004): A lower bound for the Wehrl entropy of quantum spin with sharp high-spin asymptotics, Commun. Math. Phys. 250, 287300. Uncertainty principles and optimization constitute a central theme in Bodmann’s research related to harmonic analysis and its applications. For many Hilbert spaces equipped with a reproducing kernel, it seems plausible that kernel functions should be most concentrated among all vectors. In quantum physics, this idea is often phrased as “coherent states are closest to classical”. In a previous paper, Lieb had derived a quantitative form of this statement with an entropy bound for the case of Bargmann space, as conjectured by Wehrl. In his paper, Lieb conjectured that an analogous entropy estimate should be true for the SU(2) representation spaces of Bloch coherent states. To establish an estimate of this type, Bodmann proved a variant of an inequality for Dirichlet forms by Carlen in the setting of highest weight SU(2) representations together with a sharp hypercontractivity estimate. To derive the inequality for the Dirichlet form needed for Lieb’s conjecture, Bodmann adapted techniques for finding radial solutions to quasilinear elliptic problems by Serrin and Tang. Both components, the inequalities for Dirichlet forms in holomorphic representation spaces and the radial solutions to quasilinear elliptic problems were employed by Bandyopadhyay to prove analogous results for SU(1,1). This suggests that the techniques developed by Bodmann carry over to a wider class of highest-weight Lie group representation spaces.