Dietz B, Guhr T, Gutkin B, Miski-Oglu M, Richter A
Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, D-47048 Duisburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022903. doi: 10.1103/PhysRevE.90.022903. Epub 2014 Aug 7.
We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model for systems with violated time-reversal invariance and a mixed dynamics. Furthermore, we investigate tunneling in terms of the splittings of the doublet partners. On the basis of the random-matrix model we derive an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.
我们通过使用平面超导微波谐振器测量的共振光谱，以前所未有的精度确定了两个量子常宽台球的最低900个本征值。虽然常宽台球的经典动力学是单向的，但在相应的量子系统中，通过动态隧穿，运动方向可能会发生变化。这在绝大多数共振分裂为几乎简并的双重态中表现出来。结果表明，这两个光谱各自的涨落特性与时间反演不变性被破坏且具有混合动力学的随机矩阵模型的涨落特性一致。此外，我们根据双重态伙伴的分裂来研究隧穿。基于随机矩阵模型，我们推导出了一个分裂分布的解析表达式，该表达式通常适用于在两个（主要）具有混沌动力学的区域之间表现出动态隧穿的系统。
