Strong many-particle localization by constructed disorder

这项研究的目标是研究多粒子系统中的局域化。最感兴趣的是所有多粒子态的现场定域化，有效定域化长度小于格点间距离。除了定域化外，还建议研究定域化寿命。将构建有效抑制共振跳跃的现场能量的有界序列。对于这些序列，将分析单粒子局域化跃迁，并得到衰变长度的尖锐界限。对于有限长的链，我们将研究所有多粒子态的强现场局域化。对于无限大的系统和任意数量的粒子，最感兴趣的将是局域寿命。对于弱的和强的粒子-粒子相互作用，它将被显示为格点能量带宽与格点间跃迁积分之比的高次幂。对于有限链，将考虑对能量序列进行优化，以便在给定带宽下获得最大寿命。关于位置能量误差的稳定性，长程相互作用的影响，以及由于耦合到外部储存库而产生的退相干的作用，将被研究。除了由一名物理学家和一名数学家联合开展的研究生培训外，研究课题还包括本科生的参与。参与拟议研究的学生应该从密歇根州立大学国际和平研究所组织的量子科学研究所每周一次的跨学科研讨会中受益。

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.