Kotimäki V, Räsänen E, Hennig H, Heller E J
Nanoscience Center, Department of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022913. doi: 10.1103/PhysRevE.88.022913. Epub 2013 Aug 13.
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.
尽管在诸如半导体量子点等二维系统中的混沌量子输运方面已经进行了多项实验，但到目前为止，在实空间模型内进行相应的量子模拟仍难以实现。在这里，我们对一个呈现混沌动力学的二维体育场形腔进行了实空间和实时的量子输运计算。通过施加大量的磁场，我们获得了显示分形标度的磁电导的完整图像。在分形性的计算中，我们使用了去趋势波动分析——一种在时间序列分析中广泛使用的方法——并展示了它在解释电导曲线方面的有用性。与提取分形维数的标准方法进行比较，得到了一致的结果，这些结果反过来在定性上与先前的实验数据相符。
