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揭开混乱或在经典限制中具有不可预测行为的模型系统量子现象的特定标志。 在理解此问题方面已经取得了进展，主要是针对单个粒子系统。我们建议根据受时间周期性磁场的电子相互作用的气体来考虑多体台球问题。 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为了在时间依赖的多个潜在台球中研究单个粒子混乱，我们还将在简单的依赖时间依赖的经典和量子模型的背景下探索摩擦和混乱之间的联系。