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该研究计划的目标是解开模型系统的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中具有不可预测的行为。 在理解这个问题上已经取得了进展，主要是单粒子系统。我们建议考虑的多体台球问题的相互作用气体的电子受到时间周期性磁场。 我们的初步结果表明，对于一个非相互作用的电子气的泡利排斥“力”显着修改其磁性取决于动力学是可积的或混乱的。接下来，我们将使这个问题更现实，包括库仑相互作用，经典和量子力学。 我们还将研究具有破缺旋转不变性的台球，这些台球具有“分数”角动量，有或没有恒定的外部磁场。 PI还建议研究单粒子混沌散射在时间相关的多个潜在的台球。 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，因为它解决了能量耗散，经典混沌和退相干的基本物理和概念问题，在量子计算领域的重要性。