论文标题
混乱的量子动力学的出现：Quantum Cat Maps的情况
Emergence of quantum dynamics from chaos: The case of prequantum cat maps
论文作者
论文摘要
FAURE和TSUJII最近提出了一种新的量化程序，称为“自然量化”，用于平滑的符号ANOSOV差异性。他们的方法始于前期化，这也是Kostant-Souriau-kirillov提出的几何量化的第一步，然后依靠量词传输算子的Ruelle-PolliCott Spectrum，它们显示为具有特定的频带结构。这种新量化方案的吸引力在于自然性：量子行为在量词转移操作员的经典相关函数中动态出现。在本文中，我们在$ 2N $维的圆环上明确处理了CAT地图的情况，特别表明结果等于通常的Weyl量化。我们还提供了所有Quantum Cat Maps的混凝土结构。
Faure and Tsujii have recently proposed a novel quantization procedure, named natural quantization, for smooth symplectic Anosov diffeomorphisms. Their method starts with prequantization, which is also the first step of geometric quantization as proposed by Kostant-Souriau-Kirillov, and then relies on the Ruelle-Pollicott spectrum of the prequantum transfer operator, which they show to have a particular band structure. The appeal of this new quantization scheme resides in its naturalness: the quantum behavior appears dynamically in the classical correlation functions of the prequantum transfer operator. In this paper, we explicitly work out the case of cat maps on the $2n$-dimensional torus, showing in particular that the outcome is equivalent to that of the usual Weyl quantization. We also provide a concrete construction of all the prequantum cat maps.
