CAREER: Quantum Fluctuations, Entanglement and the Casimir Effect

技术总结这一职业奖项支持利用数学物理和场论的方法进行理论研究，以解决凝聚态物理中量子涨落的基本特征及其与几何的相互作用。这项研究涉及凝聚态物理、数学物理和量子信息理论。这项研究有三个主要推动力，每一个都涉及到发展新的方法和思想：1)多体态的纠缠结构，特别关注凝聚态系统，如拓扑绝缘体和量子霍尔态。这包括纠缠、尺度和光谱。2)量子涨落及其通过Casimir效应与边界的相互作用。这包括研究物质辐射纠缠的作用，以及在耗散物质存在时Casimir力的方向。3)拓扑态及其与涨落的相互作用。这样的研究对拓扑量子计算的思想具有重要的意义。拟议中的研究对科学的更广泛影响是促进理论物理的分支之间的整合，如量子场论、统计力学和量子信息理论与数学活跃的领域，如拓扑学和泛函分析，以丰富这两个学科，并揭示它们之间的联系。此外，这项研究与现代物理学前沿正在进行的实验工作有关。例如，在设计纳米机械结构时，卡西米尔力的研究被认为是至关重要的。拓扑相在拓扑量子计算中具有潜在的应用前景，有望存在于分数量子霍尔系统中。教育部分包括通过引入新的和令人兴奋的问题和技术，向研究生介绍理论凝聚态中的现代问题。国际和平研究所将从凝聚态的角度编写一本关于卡西米尔效应的本科生至研究生级别的高年级教科书。非技术总结这个职业奖支持理论研究，利用先进的物理和数学概念和理论方法来促进我们对以下方面的理解：(I)拓扑绝缘体，这种材料不能在其内部导电，但允许其边缘或边界上的电荷移动；(Ii)Casimir效应，一种量子力学效应，在真空中导致两个非常接近的金属板之间的吸引力，即使它们不带电荷；以及(Iii)拓扑相，这是一种新的物质状态，可能掌握制造容错量子计算机的关键，预计它将比经典的同类计算机快得多。这项研究与现代物理学前沿正在进行的实验工作有关。例如，卡西米尔力预计将更加重要，因为设备和机械的物理尺寸接近比人类头发小10万倍的尺寸。教育部分包括通过引入新的和令人兴奋的问题和技术，向研究生介绍理论凝聚态中的现代问题。国际和平研究所将从凝聚态的角度编写一本关于卡西米尔效应的本科生至研究生级别的高年级教科书。

TECHNICAL SUMMARY This CAREER award supports theoretical research that draws upon methods of mathematical physics and field theory to address fundamental features of quantum fluctuations in condensed matter physics and their interplay with geometry. The research intersects condensed matter physics, mathematical physics, and quantum information theory. The research has three main thrusts, each of which involves developing new methods and ideas: 1) The entanglement structure of many-body states with a special focus on condensed matter systems, such as topological insulators and quantum Hall states. This includes entanglement scaling and spectrum. 2) Quantum fluctuations and their interplay with boundaries through the Casimir effect. This includes research into the role of matter radiation entanglement and the direction of Casimir forces in the presence of dissipative materials. 3) Topological states and their interplay with fluctuations. Such a study is of great interest for its crucial importance to the idea of topological quantum computation. The scientific broader impact of the proposed research is to advance integration between branches of theoretical physics such as quantum field theory, statistical mechanics, and quantum information theory with mathematically active areas such as topology and functional analysis in order to enrich both disciplines and to unravel the connections between them. Furthermore, the research is related to ongoing experimental efforts at the forefront of modern physics. For example, the study of Casimir forces is projected to be of fundamental importance when designing nano-mechanical structures. Topological phases have potential application in topological quantum computing and are expected to exist in fractional quantum hall systems. The educational component involves introducing graduate students to modern problems in theoretical condensed matter through the introduction of new and exciting problems and techniques. The PI will write an upper undergraduate to graduate level textbook on the Casimir effect from a condensed matter perspective. NON-TECHNICAL SUMMARY This CAREER award supports theoretical research that draws on advanced physical and mathematical concepts and theoretical methods to advance our understanding of (i) topological insulators, which are materials that cannot conduct electricity in their interior but allow movement of charges on their edges or boundaries, (ii) Casimir effect, a quantum mechanical effect that leads to attraction between two very closely spaced metallic plates in vacuum, even though they have no electric charge, and (iii) topological phases, which are new states of matter which may hold the key to making a fault-tolerant quantum computer expected to be much faster than its classical counterpart. This research is connected to ongoing experimental efforts at the forefront of modern physics. For example, Casimir forces are expected to be more important as the physical dimensions of devices and mechanisms approach dimensions some 100,000 times smaller than a human hair. The educational component involves introducing graduate students to modern problems in theoretical condensed matter through the introduction of new and exciting problems and techniques. The PI will write an upper undergraduate to graduate level textbook on the Casimir effect from a condensed matter perspective.