Theoretical Studies of Quantum Chaos

本研究计划的目标是揭示在经典极限下混沌或具有不可预测行为的模型系统的量子现象的具体特征。在理解这个问题上已经取得了进展，主要是针对单粒子系统。我们建议考虑多体台球问题，在一个相互作用的气体的电子受到时间周期磁场。我们的初步结果表明，对于非相互作用的电子气体，泡利不相容“力”会根据动力学是可积的还是混沌的显著改变其磁性。接下来，我们将使这个问题更加现实，包括经典和量子力学的库仑相互作用。我们还将研究具有破碎旋转不变性的台球，它具有“分数”角动量，有或没有恒定的外部磁场。PI还提出了对时变多势台球中单粒子混沌散射的研究。我们还将探讨摩擦和混沌之间的联系，在简单的时间依赖的经典和量子模型的背景下。这是一个重要的问题，因为它解决了在量子计算领域中重要的能量耗散、经典混沌和退相干的基本物理和概念问题。

0070977Jose The goal of this research program is to unravel specific hallmarks of quantum phenomena of model systems that are chaotic or have unpredictable behavior in the classical limit. Progress has been made in understanding this problem, mostly for single particle systems. We propose to consider the many-body billiard problem in terms of an interacting gas of electrons subjected to time-periodic magnetic fields. Our initial results indicate that for a noninteracting electron gas the Pauli exclusion ``force" significantly modifies its magnetic properties depending if the dynamics is integrable or chaotic. We will next make this problem more realistic and include the Coulomb interactions, both classically and quantum mechanically. We will also study billiards with broken rotational invariance that have``fractional'' angular momentum with or without constant external magnetic fields. The PI also proposes to study single particle chaotic scattering in time-dependent multiple potential billiards. We will also explore the connections between friction and chaos, in the context of simple time-dependent classical and quantum models. This is an important problem since it addresses the basic physical and conceptual question of energy dissipation, classical chaos, and decoherence, of importance in the field of quantum computation.