CAREER: Holography, Quantum Information, and Elliptic Relativity

该项目包括两个研究方案，探讨弦理论、经典和量子引力与其他物理领域，特别是量子信息理论、粒子和核物理学密切相关的问题：a）通过量子信息理论的透镜，研究全息系统的热和统计物理学，以及更普遍的量子引力;处理解禁闭相变和纠缠熵的方面，和波动耗散率，在时间依赖的系统。这些问题对于理解强耦合介质（如夸克-胶子等离子体）中的热化过程非常重要。B）继续发展数值求解椭圆爱因斯坦方程的实用、通用方法，以找到高维黑洞和紧化空间的静态、稳态和欧几里得度量。这样的解在弦理论的形式和唯象方面，在相关的数学问题，以及凝聚态、流体和核物理的全息模型中都扮演着重要的角色。更广泛的影响：本科研究是这两个研究项目的组成部分。三个推广，指导和物理教育活动也包括在内：理论网是一个国家科学基金会资助的计划，其中高能物理学家访问高中科学教室。PI正在参与，并建议除了教授外，还包括博士后和研究生。布兰代斯科学波塞计划是一个领导力计划，面向来自贫困背景的科学导向的本科生，它使用集中的培训和指导策略。PI将在培训和指导方面做出贡献。PI计划根据研究生水平的互动和同伴指导调整教学策略，开发评估工具，并在研究生量子力学课程中将新方法与传统的基于讲座的方法进行对照实验。

This project includes two programs of research that explore issues in string theory and classical and quantum gravity with close connections to other areas of physics,especially quantum information theory and particle and nuclear physics:a) A study of the thermal and statistical physics of holographic systems, and quantum gravity more generally, through the lens of quantum information theory; adressing aspects of the deconfinement phase transition and of entanglement entropy, and fluctuation-dissipation ratios, in time-dependent systems. These issues are important for understanding the process of thermalization in strongly-coupled media such as the quark-gluon plasma. b) Continuing the development of practical, general methods for numerically solving the elliptic Einstein equation to find static, stationary, and Euclidean metrics for higher-dimensional black holes and compactification spaces. Such solutions play an important role in both formal and phenomenogical aspects of string theory, in related mathematical issues, and in holographic models of condensed-matter, fluid, and nuclear physics.Broader impacts: Undergraduate research is an integral part of both research programs. Three outreach, mentoring, and physics education activities are also included: TheoryNet is an NSF-funded program in which high-energy physicists visit high-school science classrooms. The PI is participating, and proposes to include postdocs and graduate students in addition to professors. The Brandeis Science Posse Program is a leadership program for science-oriented undergraduates from underprivileged backgrounds, which uses focused training and mentoring strategies. The PI will contribute to both the training and the mentoring aspects. The PI plans to adapt teaching strategies based on interaction and peer instruction to the graduate level, develop assessment tools, and perform a controlled experiment comparing the new methods to conventional lecture-based ones in a graduate quantum-mechanics course.