Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators
Alix DeleporteInstitut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
We prove several results of concentration for eigenfunctions in Toeplitz quantization. Under mild regularity assumptions, we prove that eigenfunctions are away from the corresponding level set of the symbol, where is the inverse semiclassical parameter and depends on the regularity. As an application, we prove a precise bound for the free energy of spin systems at high temperatures, sharpening a result of Lieb.
Cite this article
Alix Deleporte, Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators. Doc. Math. 25 (2020), pp. 1315–1351DOI 10.4171/DM/778