论文标题
Toeplitz操作员的禁区中的分数指数衰减
Fractional exponential decay in the forbidden region for Toeplitz operators
论文作者
论文摘要
我们证明了toeplitz量化中本征素器浓度的几个结果。有了对规律性的轻度假设，我们证明eigenfunctions是$ o（exp（-cn^δ））$远离符号的相应级别集，其中n是反向半经典参数，$ 0 <Δ<1 $取决于规律性。作为一种应用，我们证明了在高温下自旋系统的自由能的精确绑定，从而使LIEB的结果锐化。
We prove several results of concentration for eigenfunctions in Toeplitz quantization. With mild assumptions on the regularity, we prove that eigenfunctions are $O(exp(-cN^δ))$ away from the corresponding level set of the symbol, where N is the inverse semiclassical parameter and $0 < δ< 1$ 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.
