论文标题
开放量子图的Weyl定律
Weyl Laws for Open Quantum Maps
论文作者
论文摘要
我们发现在半经典极限的量子开放式面包师地图的Weyl上限。对于环中的特征值数量，我们得出了渐近上限$ \数学$（n^δ）$，其中$δ$是面包师地图的陷阱集的维度和$（2πn）^{ - 1} $是$ $ \ \ \ n^$（n N）的$（2πn）^{ - 1} $是$（NAS）的$（NE）。此外，我们得出了一个Weyl上界，具有明确的依赖性对环的内半径，用于量子开放式面包师的地图，并带有Gevrey截止。
We find Weyl upper bounds for the quantum open baker's map in the semiclassical limit. For the number of eigenvalues in an annulus, we derive the asymptotic upper bound $\mathcal O(N^δ)$ where $δ$ is the dimension of the trapped set of the baker's map and $(2 πN)^{-1}$ is the semiclassical parameter, which improves upon the previous result of $\mathcal O(N^{δ+ ε})$. Furthermore, we derive a Weyl upper bound with explicit dependence on the inner radius of the annulus for quantum open baker's maps with Gevrey cutoffs.
