Meenakshisundaram N, Lakshminarayan Arul
Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):065303. doi: 10.1103/PhysRevE.71.065303. Epub 2005 Jun 28.
We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasiperiodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to the Thue-Morse sequence and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.
我们分析了量子面包师映射的某些本征态，并利用沃尔什-哈达玛变换证明了普遍存在的图厄-摩尔斯序列的出现，这是一个简单的序列，处于准周期性和混沌的边界，因此是量子混沌态的一个很好的范例。我们展示了一族也与图厄-摩尔斯序列简单相关的态，它们被短周期轨道及其同宿轨道强烈地“疤痕化”。我们给出了这些态的近似表达式，并提供证据表明这些态以及其他一般态是多重分形的。
