Collaborative Research: Quantum Vaccum Energy

合作研究：量子真空能

• 批准号: 0968269
• 负责人: Stephen Fulling
• 金额: $ 29.1万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0968269&HistoricalAwards=false
• 关键词: Collaborative; Research; Quantum; Vaccum; Energy

Vacuum (Casimir) energy in quantum field theory is of interest in the physics community and its connections with some mathematical topics in spectral theory and asymptotics of differential operators have recently become clearer. Thus this collaboration between physicists and mathematicians is an effective approach to further progress. The investigators intend to build on the results of their previous collaboration to make progress in two areas: (1) Gravitational significance of vacuum energy: The previous work has demonstrated that vacuum energy gravitates just as does any other form of energy. For plane geometries the divergences renormalize the masses of the material bodies confining the field. This analysis will be extended to general geometries. This requires the mathematical theory of the asymptotics of (Schwartz) distributions as well as sound physics. (2) Improved calculational methods: In the presence of curved surfaces, higher-order corrections are hard to calculate in classical-path analyses of vacuum energy and eigenvalue distribution. In the presence of sharp edges or corners (other than right angles) the semiclassical methods break down quite seriously (diffraction). The project will develop and apply more fundamental and accurate analyses, known as multiple reflection or multiple scattering. Previous success in treating the forces between dielectric bodies by multiple scattering will be extended and applications to practical configurations such as noncontact gears and multilayer surfaces are being pursued. Also, the multiple-reflection expansion will be used for accurate calculation of vacuum energy density and pressure near curved surfaces and edges and corners.The broader impact of the project stems partly from its interdisciplinary nature. The subject not only combines physics and mathematics, but also combines topics within physics and within mathematics that are ripe for productive interaction. Vacuum energy is relevant both to new nanotechnological devices and to cosmological issues (dark energy). Mathematically, the connection between periodic-orbit theory and vacuum energy has only recently been exploited, and the implications of vacuum energy for spectral theory have barely been explored. Undergraduate and graduate student research assistants from both physics and mathematics will be recruited and their educations will be enhanced, and a diverse student population is being trained. The project will also foster future research interactions with other fields (gravitational implications, nanotechnology, quantum graphs, spectral geometry).

量子场论中的真空（Casimir）能量是物理学界的兴趣，它与谱理论和微分算子渐近中的一些数学主题的联系最近变得更加清晰。因此，物理学家和数学家之间的这种合作是取得进一步进展的有效途径。研究人员打算在之前合作的基础上，在两个领域取得进展：（1）真空能量的引力意义：之前的工作已经证明，真空能量就像任何其他形式的能量一样具有引力。对于平面几何，发散使限制场的物质体的质量重新正规化。这一分析将扩展到一般的几何形状。这需要数学理论的渐近（施瓦茨）分布以及健全的物理。(2)改进的计算方法：在真空能量和本征值分布的经典路径分析中，由于曲面的存在，高阶修正难以计算。在存在尖锐的边缘或角落（除了直角）的半经典方法崩溃相当严重（衍射）。该项目将开发和应用更基本和更准确的分析，称为多重反射或多重散射。以前的成功治疗电介质体之间的力的多重散射将被扩展和应用到实际的配置，如非接触齿轮和多层表面正在追求。此外，多次反射展开将用于精确计算曲面和棱角附近的真空能量密度和压力。该项目更广泛的影响部分源于其跨学科性质。该主题不仅结合了物理学和数学，而且还结合了物理学和数学中的主题，这些主题已经成熟，可以进行富有成效的互动。真空能量与新的纳米技术设备和宇宙学问题（暗能量）都有关。在数学上，轨道理论和真空能量之间的联系直到最近才被利用，而真空能量对光谱理论的影响几乎没有被探索过。将招聘物理和数学专业的本科生和研究生研究助理，加强他们的教育，并培养多样化的学生群体。该项目还将促进未来与其他领域（引力影响，纳米技术，量子图形，光谱几何）的研究互动。