ARITHMETIC QUANTUM UNIQUE ERGODICITY FOR SYMPLECTIC LINEAR MAPS OF THE MULTIDIMENSIONAL TORUS
ARITHMETIC QUANTUM UNIQUE ERGODICITY FOR SYMPLECTIC LINEAR MAPS OF THE MULTIDIMENSIONAL TORUS
复制标题
多维环面辛线性图的算术量子唯一遍历性
DOI：
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发表时间：
2005
期刊：
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通讯作者：
Dubi Kelmer
中科院分区：
文献类型：
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作者：
Dubi Kelmer
我们期待在多维环面上的量子化线性辛映射的期望值和它们的分布在半经典极限。我们构建的超级疤痕是稳定的算术对称下的系统和本地化不变流形。我们证明了这些超疤痕存在时，只有有各向同性的有理子空间，线性映射下不变。在不存在这种疤痕的情况下，我们计算了去对称化系统矩阵元涨落的方差，并对它们的极限分布提出了一个猜想。
We look at the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribu- tion in the semiclassical limit. We construct super-scars that are stable under the arithmetic symmetries of the system and localize on invariant manifolds. We show that these super-scars exist only when there are isotropic rational subspaces, invariant under the linear map. In the case where there are no such scars, we com- pute the variance of the fluctuations of the matrix elements for the desymmetrized system, and present a conjecture for their limiting distributions.