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。本研究主要有三个方面：（1）。封闭量子系统中的猝灭动力学及其在冷原子气体和固态系统的全快泵浦探测光谱学中的应用。PI将建立在她最近的工作中，一种新的重整化群方法来研究临界点附近强相关系统的动力学。PI旨在推广这种方法来研究：一维系统，其中存在无序和相互作用，在更高的空间维度中量子猝灭，以及一种新的动力学相变，其中热力学极限中的封闭量子系统在其时间演化过程中表现出非分析行为。2）。光-物质耦合系统，其中二能级系统与光子之间的相互作用可以有效地导致光子的强关联态。PI将包括强驱动和耗散，这出现在这些系统的实验实现，在这些系统的研究。PI将探索不同类型的非马尔可夫耗散环境如何影响相关态的物理性质。纳米级系统中的传输。非微扰方法，如1/N展开技术将被用来研究欠屏蔽近藤模型，其中自旋大得多1耦合到载流引线。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和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性质，例如远离稳定平衡的原子小组件。当量子力学系统受到短时间的强力作用，导致系统随时间迅速变化时，通常会产生这种非平衡态。重要的问题是，系统如何随时间变化，以及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受到持续的外力作用。大型和复杂的系统，尽管施加了稳定的力，但可以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不寻常的性质，在与周围环境平衡的系统中不会遇到。PI计划在这两种失衡的情况下探索量子系统。失去平衡的系统是具有挑战性的研究课题; PI将开发新的理论技术，以促进对这些无处不在的系统的理解。在基础层面上理解失衡系统对于技术进步非常重要，例如对于未来器件的开发，这些器件将是纳米尺寸的，如分子，并且将通过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。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。项目的结果将由学生和PI在学校、讲习班和会议上介绍。此外，PI还将参加外展活动，这些活动是纽约大学物理系与当地学校之间持续伙伴关系的一部分。

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.