Strong many-particle localization by constructed disorder

构造无序的强多粒子定位

• 批准号: 0555346
• 负责人: Mark Dykman
• 金额: $ 27.4万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0555346&HistoricalAwards=false
• 关键词: Strong; many; particle; localization; constructed

The goal of the proposed research is to study localization in a many-particle system. Of central interest is on-site localization of all many-particle states, with effective localization length smaller than the intersite distance. Besides localization of stationary states, it is proposed to study the localization lifetime. Bounded sequences of on-site energies will be constructed that efficiently suppress resonant hopping. For these sequences, the single-particle localization transition will be analyzed and sharp bounds on the decay length will be obtained. Strong on-site localization of all many-particle states will be studied for a finite length chain. For an infinite system and an arbitrary number of particles, of primary interest will be the localization lifetime. It will be shown to scale as a high power of the ratio of the bandwidth of site energies to the intersite hopping integral, both for weak and strong particle-particle interaction. For a finite chain, optimization of the energy sequence in order to obtain maximal lifetime for a given bandwidth will be considered. Stability with respect to errors in site energies, the effect of long-range interaction, and the role of decoherence due to coupling to an external reservoir will be studied. In addition to graduate training, carried out jointly by a physicist and a mathematician, the research topic includes undergraduate participation. The students involved in the proposed research should benefit from a weekly interdisciplinary seminar of the Institute for Quantum Sciences organized by the PI at MSU.

该研究的目标是研究多粒子系统中的局部化问题。中心的兴趣是现场本地化的所有多粒子状态，有效的本地化长度小于intersite距离。除了定态的局域化外，还提出了研究定态寿命的方法。有界序列的现场能量将被构建，有效地抑制共振跳跃。对于这些序列，单粒子的本地化过渡将进行分析，并将得到衰减长度的急剧限制。我们将研究有限长链中所有多粒子态的强在位局域化。对于一个无限大的系统和任意数量的粒子，主要的兴趣将是本地化寿命。对于弱的和强的粒子-粒子相互作用，它将被证明与位点能量带宽与位点间跳跃积分之比的高次幂成比例。对于一个有限的链，优化的能量序列，以获得最大的寿命为给定的带宽将被考虑。稳定性方面的错误，在网站的能量，远程相互作用的影响，和退相干的作用，由于耦合到外部水库将进行研究。除了由一名物理学家和一名数学家联合进行的研究生培训外，研究课题还包括本科生的参与。参与拟议研究的学生应受益于密歇根州立大学PI组织的量子科学研究所每周一次的跨学科研讨会。