We investigate the classical scattering dynamics of the driven elliptical billiard. Two fundamental scattering mechanisms are identified and employed to understand the rich behavior of the escape rate. A long-time algebraic decay which can be tuned by varying the driving amplitude is established. Pulsed escape rates and decelerated escaping particles are generic properties of the harmonically breathing billiard. This suggests time-dependent billiards as prototype systems to study the nonequilibrium evolution of classical ensembles encountering a multitude of scattering processes off driven targets.
The relation between the Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system give equivalent effects to the Shannon entropy.
Resonance states of the 3-disk scattering system are presented for the first Casati wave number $k \approx 912$ and the second Casati wave number $k \approx 91242$. They show multifractal structure in phase space, similar to the pioneering work by Casati et al. [Physica D 131, 311 (1999)] for an open chaotic quantum map. In position space we observe scarring along segments of rays, related to multifractality and universal fluctuations, as recently found for dielectric cavities. To the best of our knowledge this resonance state at the second Casati wave number has a much larger wave number than…
We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system we chose a billiard with a 60 degree sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size and position. The spectral properties of generic quantum systems of which the classical counterpart is either…
H ${\acute{e}}$ non [8]使用倾斜台球来研究在卫星相遇和其他情况下发生的混沌散射的方面。他的模型由一个分段映射组成，描述了一个点粒子在两个圆盘上弹性弹跳的运动。从给定的高度出发，得到了一个单参数的轨道族，称为h-轨道。我们得到的逃逸分布的h-轨道的解析表达式，这也是从数值模拟的结果进行比较。最后，讨论了h轨道在Hill问题中的可能应用。
We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space, after separating the regular and chaotic eigenstates, in the regime of slightly distorted circle billiard where the classical transport time in the momentum space is still large enough, although the diffusion is not normal. In quantum systems with discrete energy spectrum the Heisenberg time $t_H =2π\hbar/ΔE$, where $ΔE$ is the mean level spacing, is an important time scale.The classical transport time scale $t_T$ in relation to the Heisenberg time scale $t_H$ (their ratio is the parameter $…
