Classical and quantum dynamics of time-dependent billiards

我们研究了时变台球的非线性经典和量子动力学，重点研究了逃逸和发射速率以及输运性质。对驱动台球的基本动力学机制进行了详细的识别和分析。我们的研究旨在控制和制备由驱动台球发射或通过驱动台球传输的粒子群和/或建议驱动台球作为可调的粒子源。为此，我们探索了大量的设置，包括不同的台球几何形状（椭圆、椭圆形、体育场）和它们的边界（谐波单频、多频和随机）的驱动规律，以及硬壁和软壁电位。量子物理将通过发展和应用波包传播方法结合复杂的吸收势来研究。可以预见，由于驱动而产生的新现象将增强对被驱动系统动力学的理解。主要的焦点是在非相互作用粒子的情况下，但相互作用的少粒子台球也将被考虑，首先是经典的，作为一个长期的角度，也量子力学。与实验小组的密切联系是存在的，并将在项目的发展过程中提出。

We investigate the nonlinear classical and quantum dynamics of time-dependent billiards with the focus on escape and emission rates as well as transport properties. The fundamental dynamical mechanisms of driven billiards will be identified and analyzed in detail. Our studies aim at the control and preparation of ensembles of particles emitted from or transported through driven billiards and/or at suggesting the driven billiards as tunable sources of particles. To this end we explore a significant number of setups including different billiard geometries (ellipse, oval, stadium) and driving laws of their boundaries (harmonic single frequency, multi-frequency and stochastic) as well as hard versus soft-wall potentials. The quantum physics will be investigated by developing and applying wave packet propagation methods combined with complex absorbing potentials. It is foreseeable that novel phenomena due to the driving will enhance the understanding of the dynamics of driven systems in general. The primary focus is on the case of non-interacting particles but interacting few-particle billiards will be considered too, first classically and as a long-term perspective also quantum mechanically. A close contact to experimental groups exists and will be put forward in the course of the evolution of the project.