Semiclassical Approach to Spectral Statistics of Interacting Quantum Many-Body Systems

相互作用量子多体系统谱统计的半经典方法

• 批准号: 402552305
• 负责人: Professor Dr. Karl Thomas Guhr
• 金额: --
• 依托单位: Forschungsgruppe Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/402552305?language=en
• 关键词: Semiclassical; Approach; Spectral; Statistics; Interacting

In recent years, the study of interacting many-body systems has made considerable progress. An improved understanding of many-body localization on the theoretical sideis paired with recent cold-atom experiments allowing the fabrication and the control of interacting many-body systems. To comprehend ever better the dynamics of interacting many-body systems is a central task in many research fields including condensed matter physics, nuclear physics and quantum optics.The aim of this proposal is to characterize the spectral statistics (i.e. spectral correlations) of interacting quantum many-body systems. Understanding the connection between the spectral statistics and the classical dynamics for single-particle systems has been subject of intensive research during the last decades in the research field of quantum chaos. However, for a many-body system new features arise for example due to indistinguishability and the bosonic or fermionic character of the particles. Particularly important for the spectral statistics is also the issue of collective motion as opposed to incoherent motion of the individual particles. A deeper theoretical understanding is difficult as the lines of reasoning developed in quantum chaos cannot simply be carried over from one to many particles when considering collectivity. Building on our recent work we want to study this challenging problem, starting from spin chains which presently receive much interest in theory and experiment. We also aim at first steps to extend our study to a broader class of interacting many-body systems.

近年来，多体系统相互作用的研究取得了长足的进展。理论方面对多体定位的进一步理解与最近的冷原子实验相结合，允许制造和控制相互作用的多体系统。更好地理解相互作用的多体系统的动力学是包括凝聚态物理、核物理和量子光学在内的许多研究领域的中心任务。该提案的目的是表征相互作用的量子多体系统的光谱统计（即光谱相关性）。了解单粒子系统的光谱统计与经典动力学之间的联系是过去几十年量子混沌研究领域深入研究的主题。然而，对于多体系统来说，由于粒子的不可区分性以及玻色子或费米子特性，会出现新的特征。对于光谱统计来说特别重要的是集体运动问题，而不是单个粒子的不相干运动。更深入的理论理解是困难的，因为在考虑集体时，量子混沌中发展的推理路线不能简单地从一个粒子转移到多个粒子。在我们最近的工作基础上，我们希望从目前在理论和实验中引起广泛关注的自旋链开始研究这个具有挑战性的问题。我们的第一步还旨在将我们的研究扩展到更广泛的相互作用的多体系统。