English

Fractional exponential decay in the forbidden region for Toeplitz operators

Spectral Theory 2020-01-23 v1

Abstract

We prove several results of concentration for eigenfunctions in Toeplitz quantization. With mild assumptions on the regularity, we prove that eigenfunctions are O(exp(cNδ))O(exp(-cN^{\delta})) away from the corresponding level set of the symbol, where N is the inverse semiclassical parameter and 0<δ<10 < \delta < 1 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.

Keywords

Cite

@article{arxiv.2001.07921,
  title  = {Fractional exponential decay in the forbidden region for Toeplitz operators},
  author = {Alix Deleporte},
  journal= {arXiv preprint arXiv:2001.07921},
  year   = {2020}
}
R2 v1 2026-06-23T13:17:26.219Z