CAREER: Quantum many-body physics beyond the Boltzmann paradigm: prethermalization, many-body localization, and their applications

非技术总结材料研究部和物理部为这一职业奖提供资金，该奖项支持关于由许多相互作用的粒子组成的量子系统动力学的理论研究和教育。该项目探索了需要异常长时间才能达到热平衡(或者在某些极端情况下，从未达到平衡)的量子系统。达到平衡的方法涉及到系统“忘记”关于其初始状态的信息。例如，如果一种气体最初被放在管子的左侧，然后被允许在整个管子中扩散，它最终会忘记它是从哪一边开始的。这种明显的“遗忘”与量子力学定律相抵触，量子力学定律实际上保存了信息；人们相信，关于初始状态的信息永远不会被真正忘记，而是存储在复杂的、实验上无法获得的关联中。信息如何从可测量的相关性迁移到隐藏的相关性，通常还不清楚。这个项目从与眼镜相关的物质状态的角度来探讨这个普遍的问题，在这种状态下，“遗忘”是极其缓慢的。在中间政权中，系统的一些部门处于平衡状态，而另一些部门则远未达到平衡。需要用新的理论方法来概括传统的统计力学，来描述这些中间机制。开发这种方法并利用它们来确定这些中间制度的显著特征是该项目的主要目标。该项目的另一个主要关注点是将缓慢平衡系统用于新的量子应用，包括热机、量子存储器和传感器。由于平衡对应于信息的遗忘或隐藏，平衡缓慢的系统保留信息的时间很长；这一观察结果奠定了本项目将探索的各种应用的基础。这个项目将在斯塔滕岛学院进行，该学院有一个多样化的学生群体，包括很大比例的第一代大学生、代表性不足的少数族裔和最近的移民。教育活动将包括制定课程，使物理与这一广泛的学生相关，包括重新调整标准课程的方向，以强调在各种专业中有用的通用计算方法，以及开发关于复杂系统的新课程。与更广泛的社区的接触将包括开发一个迷你博物馆，通过简单的互动展品展示日常生活中的普遍现象。技术总结材料研究部和物理部为这一职业奖项提供资金，该奖项支持关于相互作用的量子系统性质的理论研究和教育，这些相互作用的量子系统异常缓慢地接近热平衡：即其热化时间标度比其他内在时间标度长得多的系统。这些系统包括几乎可积或几乎多体局域的孤立系统，以及相关的开放系统。这个项目的主要目标有三个：开发适合于缓慢热化系统的计算方法，表征这种系统中分布函数的独特的非热特征，并将这些独特的特征应用于量子技术。第一个主要目标是开发描述缓慢加热系统的动力学的方法。由于纠缠的增长，现有的方法通常限于短时间和/或小系统。该项目将开发适合缓慢加热系统的中后期行为的方法。具体地说，预热化区域的场论，以及平均场和重整化群技术，它们利用相互作用和热化之间的时间尺度分离来描述热行为的出现。这些方法将应用于涉及几乎可积(一维偶极气体)或多体局域的超冷原子系统的实验。第二个主要目标是描述缓慢热化系统中物理可观测量的概率分布，重点是多体局部化。这样的分布预计是厚尾的；这个项目将描述这些尾巴的特征，以及它们对诸如非线性响应等可观测的影响。第三个主要目标是探索非热化系统(再次关注多体局域情况)在量子信息科学、量子计量学和量子热力学中的应用。这个项目将在斯塔滕岛学院进行，该学院有一个多样化的学生群体，包括很大比例的第一代大学生、代表性不足的少数族裔和最近的移民。教育活动将包括制定课程，使物理与这一广泛的学生相关，包括重新调整标准课程的方向，以强调在各种专业中有用的通用计算方法，以及开发关于复杂系统的新课程。与更广泛的社区的接触将包括开发一个迷你博物馆，通过简单的互动展品展示日常生活中的普遍现象。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Physics contribute funds to this CAREER award, which supports theoretical research and education on the dynamics of quantum systems made up from many interacting particles. The project explores quantum systems that take anomalously long to approach thermal equilibrium (or, in some extreme cases, never approach equilibrium). The approach to equilibrium involves a system "forgetting" information about its initial state. For example, if a gas is initially put in the left side of a tube, and then is allowed to spread throughout the tube, it eventually forgets which side it started out in. This apparent "forgetting" is at odds with the laws of quantum mechanics, which in fact conserve information; it is believed that information about the initial state is never truly forgotten, but is stored in complicated, experimentally inaccessible correlations. How information migrates from measurable to hidden correlations is in general not understood. This project approaches the general question from the perspective of states of matter related to glasses, in which "forgetting" is extremely slow. In the intermediate regimes, some sectors of the system are in equilibrium, whereas others are far from it. New theoretical methods that generalize conventional statistical mechanics are required to characterize these intermediate regimes. Developing such methods and using them to identify distinctive features of these intermediate regimes are primary objectives of this project. The other major focus of this project is to use slowly equilibrating systems for novel quantum applications, including heat engines, quantum memories, and sensors. Since equilibration corresponds to the forgetting or hiding of information, systems that are slow to equilibrate retain information for very long times; this observation underlies the various applications that will be explored in this project. This project will take place at the College of Staten Island, which has a diverse student body including large proportions of first-generation college students, underrepresented minorities, and recent immigrants. Educational activities will include curricular development to make physics relevant for this wide range of students, including the reorientation of standard courses to emphasize general-purpose computational methods, which are useful in a wide range of professions, as well as development of new courses on complex systems. Outreach to the broader community will involve developing a mini museum that will illustrate universal phenomena in everyday life through simple interactive exhibits. TECHNICAL SUMMARYThe Division of Materials Research and the Division of Physics contribute funds to this CAREER award, which supports theoretical research and education on the properties of interacting quantum systems that approach thermal equilibrium anomalously slowly: i.e., systems for which the thermalization timescale is much longer than other intrinsic timescales. These include isolated systems that are nearly integrable or nearly many-body localized, as well as related open systems. The main goals of this project are threefold: to develop computational methods suited to slowly thermalizing systems, to characterize distinctively non-thermal features of distribution functions in such systems, and to apply these distinctive features to quantum technologies. The first main goal is to develop methods to describe the dynamics of slowly thermalizing systems. Existing approaches are typically limited to short times and/or small systems, owing to the growth of entanglement. This project will develop methods tailored to the intermediate and late-time behavior of slowly thermalizing systems. Specifically, field theories of the prethermalized regime, as well as mean-field and renormalization-group techniques that leverage the separation of timescales between interactions and thermalization to describe the emergence of thermal behavior. These methods will be applied to experiments involving ultracold atomic systems that are nearly integrable (one-dimensional dipolar gases) or many-body localized. The second main goal is to characterize the probability distributions of physical observables in slowly thermalizing systems, focusing on many-body localization. Such distributions are expected to be fat-tailed; this project will characterize these tails, and their implications for observables such as the nonlinear response. The third main goal is to explore applications of non-thermalizing systems (again, focusing on the many-body localized case) for quantum information science, quantum metrology, and quantum thermodynamics. This project will take place at the College of Staten Island, which has a diverse student body including large proportions of first-generation college students, underrepresented minorities, and recent immigrants. Educational activities will include curricular development to make physics relevant for this wide range of students, including the reorientation of standard courses to emphasize general-purpose computational methods, which are useful in a wide range of professions, as well as development of new courses on complex systems. Outreach to the broader community will involve developing a mini museum that will illustrate universal phenomena in everyday life through simple interactive exhibits.