论文标题
几乎最大开放量化的猫图的光谱
The Spectrum of an Almost Maximally Open Quantized Cat Map
论文作者
论文摘要
我们考虑量化猫图的特征值（即双曲线符号整数矩阵），切断相空间，以将固定点作为圆环上唯一的周期轨道。我们证明了在量化的真实线和量化的圆环上的特征值的简单公式，即半经典限制为$ h \ to0 $。然后，我们考虑没有固定点的情况，并证明了在特征值上绑定的超多种衰减。结果用数值计算说明了结果。
We consider eigenvalues of a quantized cat map (i.e. hyperbolic symplectic integer matrix), cut off in phase space to include a fixed point as its only periodic orbit on the torus. We prove a simple formula for the eigenvalues on both the quantized real line and the quantized torus in the semiclassical limit as $h\to0$. We then consider the case with no fixed points, and prove a superpolynomial decay bound on the eigenvalues. The results are illustrated with numerical calculations.
