Classical and quantum dynamics of time-dependent billiards

瞬态台球的经典和量子动力学

• 批准号: 48246955
• 负责人: Professor Dr. Peter Schmelcher
• 金额: --
• 依托单位: Zentrum für Optische Quantentechnologien (ZOQ)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/48246955?language=en
• 关键词: Classical; quantum; dynamics; time; dependent

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.

我们研究了含时台球的非线性经典和量子动力学，重点是逃逸和发射率以及输运性质。驱动台球的基本动力机制将被确定和详细分析。我们的研究旨在控制和准备合奏的粒子发射或通过驱动台球和/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（椭圆形，卵形，体育场）和他们的边界（谐波单频，多频和随机），以及硬与软壁的潜力驱动法律。量子物理学将通过发展和应用波包传播方法结合复吸收势来研究。可以预见的是，由于驱动的新现象将提高一般的驱动系统的动力学的理解。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，作为一个长期的观点，也量子力学。与实验组有密切联系，并将在项目发展过程中提出。