Theoretical Studies of Quantum Chaos

这个研究计划的目标是揭开模型系统的量子现象的具体特征，这些系统在经典极限下是混沌的或具有不可预测的行为。在理解这个问题方面已经取得了进展，主要是针对单粒子系统。我们建议用时间周期磁场作用下的电子相互作用气体来考虑多体台球问题。我们的初步结果表明，对于非相互作用的电子气，泡利排斥“力”显着地改变了它的磁性，这取决于动力学是可积的还是混沌的。接下来，我们将使这个问题变得更加现实，包括库仑相互作用，无论是经典的还是量子力学的。我们还将研究具有破缺旋转不变性的台球，这些台球在有或没有恒定外磁场的情况下具有“分数”角动量。PI还建议研究含时多势台球中的单粒子混沌散射。我们还将在简单的依赖时间的经典和量子模型的背景下，探索摩擦和混沌之间的联系。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、经典混沌和退相干等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.