Entropy of Semiclassical Measures of the Walsh-Quantized Baker’s Map
Entropy of Semiclassical Measures of the Walsh-Quantized Baker’s Map
复制标题
沃尔什量化贝克图的半经典测度的熵
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Nonnenmacher
中科院分区：
文献类型：
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作者：
N. Anantharaman;S. Nonnenmacher
摘要。我们研究贝克映射和它的沃尔什量子化，作为一个玩具模型的量子化混沌系统。我们关注半经典坐标系中本征态的局域化性质。简单的反例表明，量子唯一遍历性在该模型中不成立。然而，我们得到了与半经典测度相关的熵的下界，以及特征态的Wehrl熵的下界。这些证明的核心工具是“熵不确定性原理”。
Abstract.We study the baker’s map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization properties of eigenstates, in the semiclassical régime. Simple counterexamples show that quantum unique ergodicity fails for this model. We obtain, however, lower bounds on the entropies associated with semiclassical measures, as well as on the Wehrl entropies of eigenstates. The central tool of the proofs is an “entropic uncertainty principle”.