Collaborative Research: Quantum Vaccum Energy

合作研究：量子真空能

• 批准号: 0968492
• 负责人: Kimball Milton
• 金额: $ 32.91万
• 依托单位: University of Oklahoma Norman Campus
• 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 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0968492&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（卡西米尔）能量是物理界感兴趣的问题，它与谱理论和微分算子渐近性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。研究人员打算以他们之前的合作成果为基础，在两个领域取得进展：(1)真空能的引力意义：之前的工作已经证明真空能和任何其他形式的能量一样具有引力作用。对于平面几何，散度重整了约束场的物质体的质量。这种分析将推广到一般几何。这需要（Schwartz）分布的渐近性的数学理论以及声音物理学。(2)改进了计算方法：在存在曲面的情况下，真空能量和特征值分布的经典路径分析难以计算高阶修正。在尖锐的边缘或角（直角除外）存在的情况下，半经典方法严重失效（衍射）。该项目将发展和应用更基本和准确的分析，即多次反射或多次散射。以前通过多次散射处理介电体之间的力的成功将得到扩展，并将其应用于实际结构，如非接触齿轮和多层表面。同时，利用多重反射展开法精确计算曲面和边角处的真空能量密度和压力。该项目的广泛影响部分源于其跨学科的性质。该学科不仅结合了物理和数学，而且还结合了物理和数学中的主题，这些主题已经成熟，可以进行富有成效的互动。真空能与新的纳米技术装置和宇宙学问题（暗能量）都有关。在数学上，周期性轨道理论和真空能之间的联系直到最近才被发现，而真空能对光谱理论的影响几乎没有被探索过。将从物理学和数学领域招聘本科生和研究生研究助理，并加强他们的教育，同时正在培训多样化的学生群体。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、光谱几何）的研究互动。