Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland.
Phys Rev E. 2017 May;95(5-1):052202. doi: 10.1103/PhysRevE.95.052202. Epub 2017 May 3.
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of problems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs. This may be attributed to the unavoidable occurrence of short periodic orbits, which explore only the individual bonds forming a graph and thus do not sense the chaoticity of its dynamics. In order to corroborate our supposition, we performed numerous experimental and corresponding numerical studies of long-range fluctuations in terms of the number variance and the power spectrum. Furthermore, we evaluated length spectra and compared them to semiclassical ones obtained from the exact trace formula for quantum graphs.
我们提出了具有混沌经典动力学和时间反演不变性的量子图的谱中长程涨落特性的实验和数值结果。这些系统通常被认为为实验研究源自量子混沌和随机矩阵理论领域的问题提供了理想的基础。我们的目标是证明这仅适用于谱中的短程涨落特性，而在长程涨落中观察到的偏差是量子图的典型特征。这可能归因于短周期轨道的不可避免发生，这些轨道仅探索形成图的各个键，因此无法感知其动力学的混沌性。为了证实我们的假设，我们进行了大量的实验和数值研究，以研究数量方差和功率谱中的长程涨落。此外，我们评估了长度谱，并将其与从量子图的精确轨迹公式获得的半经典谱进行了比较。
