Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

该奖项支持理论研究和教育，以研究强相关量子系统中的非平衡现象。这项研究有三个重点：1)。封闭量子系统的猝灭动力学及其在冷原子气体和固态系统的超快泵浦探测光谱中的应用。PI将建立在她最近的工作，其中一种新的重整化群方法来研究近临界点强相关系统的动力学被开发。PI旨在推广这种方法来研究：一维系统，其中无序和相互作用都存在，更高空间维度的量子猝灭，以及一种新的动态相变，其中热力学极限的封闭量子系统在其时间演化过程中表现出非解析行为。2）. 在光-物质耦合系统中，两能级系统和光子之间的相互作用可以有效地导致光子的强相关态。在这些系统的研究中，PI将包括在这些系统的实验实现中出现的强驱动和耗散。PI将探索不同种类的非马尔可夫性质的耗散环境如何影响相关状态的物理。纳米级系统中的传输。非微扰方法，如1/N展开技术，将用于研究未屏蔽的近藤模型，其中一个大得多的自旋耦合到载流引线。该项目的这一部分与通过自旋簇的传输有关。该奖项支持研究生和本科生的积极参与，以及PI在K-12外展活动中的努力，这些活动是纽约大学物理系与当地学校之间持续合作的一部分。该奖项支持理论研究和教育，以探索量子力学系统的特性，如原子的小集合，远离平衡的稳定平衡。这种非平衡状态通常是在量子力学系统受到短时间内作用的强作用力导致系统随时间迅速变化时产生的。重要的问题出现了，系统如何随时间变化，系统需要多长时间才能最终与周围环境建立平衡。量子系统失去平衡的另一种方式是使其持续受到外力的作用。大而复杂的系统，尽管稳定地施加力，也能达到与时间无关的稳定状态。这种与时间无关的状态可能具有在与周围环境平衡的系统中不会遇到的不寻常的特性。PI计划探索这两种失衡情况下的量子系统。失衡系统是具有挑战性的研究课题；PI将开发新的理论技术来促进对这些无处不在的系统的理解。在基本层面上理解失衡系统对于技术进步非常重要，例如未来的设备将是纳米级的，就像一个分子，并且将由电流和光的流动来操纵。在这个尺度上，材料和设备之间的区别变得模糊了。该提案具有很强的教育成分，因为它将涉及研究生和本科生的积极参与。这些项目的成果将由学生和PI在学校、研讨会和会议上展示。此外，PI还将参与作为纽约大学物理系与当地学校持续合作的一部分的外展活动。

TECHNICAL SUMMARYThis award supports theoretical research and education to study of nonequilibrium phenomena in strongly correlated quantum systems. The research has three thrusts:1). Quench dynamics in closed quantum systems with applications to cold-atomic gases and toultra-fast pump-probe spectroscopy of solid-state systems. The PI will build on her recent work where a novel renormalization group approach to study the dynamics of strongly correlated systems near critical points was developed. The PI aims to generalize this approach to study: one-dimensional systems where both disorder and interactions are present, quantum quenches in higher spatial dimensions, and a new kind of dynamical phase transition where a closed quantum system in the thermodynamic limit shows non-analytic behavior during its time-evolution. 2). Light-matter coupled systems where the interaction between two-level systems and photons can effectively lead to strongly correlated states of photons. The PI will include both strong driving and dissipation, which appear in experimental realizations of these systems, in the study of these systems. The PI will explore how different kinds of dissipative environments which are non-Markovian in nature affect the physics of the correlated states.3). Transport in nanoscale systems. Nonperturbative methods such as 1/N expansion techniques will be used to study the underscreened Kondo model in which a spin much greater 1 is coupled to current carrying leads. This part of the project has relevance to transport through spin clusters.This award supports active participation of graduate and undergraduate student, and the PI's efforts in K-12 outreach activities that are part of a continuing partnership between the NYU physics department and local schools. NON-TECHNICAL SUMMARYThe award supports theoretical research and education to explore the properties of quantum mechanical systems, such as small assemblies of atoms, that are far from the steady balance of equilibrium. This nonequilbrium state often results when the quantum mechanical system has been subjected to strong forces that act for a short period of time causing the system to change rapidly with time. Important questions arise as to how the system changes in time and how long the system takes to eventually establish a balance with its surroundings. Another way for a quantum system to go out of balance is by subjecting it to a continuous application of an external force. Large and complex systems, despite the steady application of a force, can reach a steady state that is independent of time. This time-independent state can have unusual properties not encountered in systems that are in balance with their surroundings. The PI plans to explore quantum systems in these two kinds of out of balance situations. Out-of-balance systems are challenging topics to study; the PI will develop new theoretical techniques to advance understanding of these ubiquitous systems. Understanding out of balance systems at a fundamental level is important for technological advancement such as for the development of future devices that will be nanometer sized, like a molecule, and will be manipulated by the flow of electric current and by light. On this scale the distinction between material and device becomes blurred.The proposal has a strong educational component as it will involve active participation of graduate and undergraduate students. The results of the projects will be presented at schools, workshops and conferences by the students as well as the PI. In addition, the PI will participate in outreach activities that are part of a continuing partnership between the NYU physics department and local schools.