Communications in Mathematical Physics On the Maximal Scarring for Quantum Cat Map Eigenstates
Communications in Mathematical Physics On the Maximal Scarring for Quantum Cat Map Eigenstates
复制标题
量子猫图本征态最大疤痕的数学物理通讯
DOI：
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发表时间：
2004
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：
F. Faure;S. Nonnenmacher
考虑二维环面上的量子化双曲自同构（或广义量子猫映射），在半经典极限下研究其本征态在相空间中的局域化性质.我们证明了如果对应于一个归一化本征态序列的半经典测度有一个纯点分量（“强疤痕”现象），那么这个分量的权不能大于勒贝格分量的权，因此允许有一个尖锐的上界1/2.
We consider the quantized hyperbolic automorphisms on the 2-dimensional torus (or generalized quantum cat maps), and study the localization properties of their eigenstates in phase space, in the semiclassical limit. We prove that if the semiclassical measure corresponding to a sequence of normalized eigenstates has a pure point component (phenomenon of “strong scarring”), then the weight of this component cannot be larger than the weight of the Lebesgue component, and therefore admits the sharp upper bound 1/2.