混沌散射离散模型中的分形Weyl定律
Fractal Weyl laws in discrete models of chaotic scattering
摘要：
我们分析了量子混沌散射的简单模型，即量子化开贝克映射。我们数值计算了半经典系统中的量子共振密度。该密度满足分形外尔定律，其中指数由捕获轨迹集的（分形）维数决定。这种类型的行为也预计在（物理上更相关）的情况下，哈密顿混沌散射。在简化的模型中，我们能够严格证明外尔定律，并计算与通过系统的“相干传输”相关的量，即电导和“散粒噪声”。后者接近随机矩阵理论的预测。
英文摘要：
We analyze simple models of quantum chaotic scattering, namely quantized open baker's maps. We numerically compute the density of quantum resonances in the semiclassical régime. This density satisfies a fractal Weyl law, where the exponent is governed by the (fractal) dimension of the set of trapped trajectories. This type of behaviour is also expected in the (physically more relevant) case of Hamiltonian chaotic scattering. Within a simplified model, we are able to rigorously prove this Weyl law, and compute quantities related to the "coherent transport" through the system, namely the conductance and "shot noise". The latter is close to the prediction of random matrix theory.
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