CAREER: Holography, Quantum Information, and Elliptic Relativity

本项目包括两个研究项目，探索与其他物理领域，特别是量子信息理论、粒子和核物理密切相关的弦理论、经典和量子引力问题：a)通过量子信息理论的透镜研究全息系统的热物理和统计物理，以及更广泛的量子引力；在依赖时间的系统中，处理解定义相变、纠缠熵和涨落耗散比的问题。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)继续发展实用的、通用的方法，用于数值求解椭圆爱因斯坦方程，以找到高维黑洞和紧化空间的静态、平稳和欧几里得度量。这样的解决方案在弦理论的形式和现象学方面、相关的数学问题以及凝聚态物质、流体和核物理的全息模型中都发挥着重要作用。更广泛的影响：本科研究是两个研究项目的一个组成部分。三种拓展、指导和物理教育活动也包括在内：TheoryNet是nsf资助的项目，高能物理学家访问高中科学教室。PI正在参与，并提议在教授之外还包括博士后和研究生。布兰迪斯科学团队项目是一个面向来自贫困背景的理科本科生的领导力项目，采用重点培训和指导策略。项目负责人将在培训和指导方面做出贡献。PI计划将基于互动和同伴指导的教学策略调整到研究生水平，开发评估工具，并在研究生量子力学课程中进行对照实验，将新方法与传统的基于讲座的方法进行比较。

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.