Fractional exponential decay in the forbidden region for Toeplitz operators

Alix Deleporte

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arXiv · 2001.07921

Fractional exponential decay in the forbidden region for Toeplitz operators

Alix Deleporte

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Abstract

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

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BibTeX RIS

Alix Deleporte. 2020-01-22. Fractional exponential decay in the forbidden region for Toeplitz operators. https://arxiv.org/abs/2001.07921

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