Toeplitz算子禁区内的分数指数衰减

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2020-01-22 DOI:10.4171/dm/778

Alix Deleporte

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引用次数: 2

摘要

我们证明了Toeplitz量化中特征函数集中的几个结果。通过对正则性的温和假设，我们证明了特征函数$O(exp(-cN^{\delta}))$远离符号的相应水平集，其中N是逆半经典参数，$0 < \delta < 1$取决于正则性。作为一个应用，我们证明了自旋系统在高温下的自由能的精确界，锐化了Lieb的结果。

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Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators

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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来源期刊

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.