混沌本征态的熵
Entropy of chaotic eigenstates
摘要：
这些注记给出了一种研究负截面曲率紧致黎曼流形上拉普拉斯算子高频本征态的新方法。主要结果是一个下界的Kolmogorov-Sinai熵的半经典措施与序列的本征态，表明高频本征态不能太本地化。将该方法推广到半经典Hamilton算子的情形，即经典流在某些能量范围内是Anosov型的情形，以及环面上量子化Anosov同构的情形.
英文摘要：
These notes present a recent approach to study the high-frequency eigenstates of the Laplacian on compact Riemannian manifolds of negative sectional curvature. The main result is a lower bound on the Kolmogorov-Sinai entropy of the semiclassical measures associated with sequences of eigenstates, showing that high-frequency eigenstates cannot be too localized. The method is extended to the case of semiclassical Hamiltonian operators for which the classical flow in some energy range is of Anosov type, and to the case of quantized Anosov diffeomorphisms on the torus.
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