多维环面辛线性映射的算术量子唯一遍历性
Arithmetic Quantum Unique Ergodicity for Symplectic Linear Maps of the Multidimensional Torus
摘要：
我们期待的期望值的量化线性辛映射的多维环面和它们的分布在半经典极限。我们构建的超级疤痕，是稳定的算术对称的系统和本地化周围不变的流形。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。在没有疤痕的情况下，我们计算了去对称化系统的矩阵元的涨落方差，并对它们的极限分布提出了一个猜想。
英文摘要：
We look at the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribution in the semiclassical limit. We construct super-scars that are stable under the arithmetic symmetries of the system and localize around 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 compute the variance of the fluctuations of the matrix elements for the desymmetrized system, and present a conjecture for their limiting distributions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
