Chaotic Dynamics and Quantum Field Theory

该奖项资助纽约城市大学研究生院弗拉基米尔·罗森豪斯教授的研究活动。混沌是自然界中普遍存在的一种现象，它对微小的变化极其敏感，这些微小变化会在烟羽内部或在湍急流动的河流中的岩石后面引起剧烈的搅动。这个项目的目标是更好地理解混沌如何在自然界最小的尺度上表现出来，在基本粒子的水平上。过去十年的一系列发现，在高能物理、凝聚态物理和量子信息论的交汇处，揭示了混沌在最终解决物理学中最深层次的问题之一--使引力与量子力学相协调--中必须发挥的关键作用。因此，这一领域的研究通过促进科学最基本的方向之一--发现和理解新的物理定律--来促进国家利益。罗森豪斯教授将在高能粒子散射的理论计算中寻找混沌的特征，并将开发展示多体量子混沌的新模型。预计该项目还将产生更广泛的重大影响。罗森豪斯教授将指导参与研究的研究生和博士后，根据研究开发新的专题研究生课程，进行公开演讲，并组织科学研讨会。从技术上讲，罗森豪斯教授将以混沌为指导和主题，更好地理解量子场论的动力学，并将在量子场论中研究散射中的混沌。多粒子散射的不稳定行为将为量子场论中一种新的混沌测量方法提供基础，这将为近乎可积的量子场理论带来曙光。在弦理论的背景下，他将计算高激发弦的新的散射振幅，给出高能散射中的混沌的具体演示。此外，在Sachdev-Ye-Kitaev模型的基础上，将发现新的呈现多体量子混沌的大N模型，并用于深入了解强耦合量子场论中的热化和混沌。通过使用可解模型和保形场论技术，将发现量子湍流级联的新例子。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Vladimir Rosenhaus at The Graduate Center of the City University of New York.Chaos, a ubiquitous phenomenon in nature, is the extreme sensitivity to small changes which gives rise to the violent churning inside of a smoke plume or behind a rock in a rapidly flowing river. The goal of this project is to better understand how chaos manifests itself at the smallest scales in nature, at the level of fundamental particles. A web of discoveries over the past decade, at the intersection of high energy physics, condensed matter physics, and quantum information theory, have revealed the essential role chaos must play in the eventual solution of one of the deepest problems in physics, of reconciling gravity with quantum mechanics. As a result, research in this area advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical laws. Professor Rosenhaus will search for signatures of chaos in theoretical computations of high energy particle scattering and will develop new models exhibiting many-body quantum chaos. This project is also envisioned to have significant broader impacts. Professor Rosenhaus will mentor graduate students and postdocs who will be involved in the research, develop new special topics graduate courses based on the research, give public lectures, and organize scientific workshops. More technically, Professor Rosenhaus will use chaos as a guide and a theme to better understand the dynamics of quantum field theories, and will study chaos in scattering in quantum field theory. The erratic behavior of many-particle scattering will provide the basis for a new measure of chaos in quantum field theory, which will shed light on nearly-integrable quantum field theories. In the context of string theory, he will compute novel scattering amplitudes of highly excited strings, giving a concrete demonstration of chaos in high energy scattering. In addition, building on the Sachdev-Ye-Kitaev model, new large N models exhibiting many-body quantum chaos will be found and used to gain insight on thermalization and chaos in strongly coupled quantum field theories. Through use of solvable models and conformal field theory techniques, novel examples of quantum turbulent cascades will be found.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.