Theoretical Studies of Quantum Chaos

量子混沌的理论研究

• 批准号: 0070977
• 负责人: Jorge Jose
• 金额: $ 18.7万
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070977&HistoricalAwards=false
• 关键词: Theoretical; Studies; Quantum; Chaos

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.

0070977Jose 该研究项目的目标是揭示模型系统量子现象的特定特征，这些模型系统是混沌的或在经典极限下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。我们建议根据受时间周期磁场影响的相互作用的电子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”会显着改变其磁性，具体取决于动力学是可积还是混沌。接下来，我们将使这个问题更加现实，并包括库仑相互作用，无论是经典力学还是量子力学。我们还将研究具有破坏的旋转不变性的台球，这些台球在有或没有恒定外部磁场的情况下具有“分数”角动量。PI还提出 研究时间相关的多势台球中的单粒子混沌散射。 我们还将在简单的时间相关经典模型和量子模型的背景下探索摩擦与混沌之间的联系。这是一个重要的问题，因为它解决了能量耗散、经典混沌和退相干等基本物理和概念问题，这些问题在量子计算领域非常重要。