Research on Gravity and Quantum Fluctuation Effects

理论物理中许多最深层次的问题都围绕着爱因斯坦的广义相对论与量子理论的结合展开。由此产生的理论被称为量子引力，需要用来更好地理解宇宙的起源、小尺度上的空间和时间的性质，以及黑洞内部发生的事情。该奖项支持的研究将使用最新的技术和工具来尝试研究量子涨落及其影响，特别是罕见但较大的能量密度自发涨落。这些都是微妙的影响，还没有被很好地理解。这项研究的结果可能会应用到其他科学领域，也可能应用到技术领域。所要研究的大涨落可能在非线性光学和量子隧道这两个有着广泛应用的领域发挥作用。该项目还将带来教育方面的好处。学生将参与研究，并从中获得宝贵的经验。该项目还应该提供一些例子，可以用来向不同教育水平的学生解释量子理论和相对论的一些概念。该项目将调查量子应力张量涨落的概率分布及其在引力理论和其他物理领域的应用。将特别注意该分布的渐近形式，它支配着大波动的概率。要使用的一种方法是计算分布的大力矩。初步研究表明，与热分布的渐近形式相比，这种渐近形式下降得相当慢。这表明，对于大波动，量子真空效应可能会超过热效应，并表明在这一研究领域可能会发现新的物理效应。将对几个模型进行检查，以寻找这种影响。一个是辐射压力波动对电子和其他粒子的量子隧穿的影响。另一个模型将研究电场波动对光在非线性材料中传播的影响。这项研究既对光学物理感兴趣，也是对量子引力理论中预期的量子光锥波动的模拟模型。该项目还将研究量子应力张量涨落在早期宇宙中的作用，特别是在膨胀模型中。

Many of the deepest problems in theoretical physics revolve around combining Einstein's theory of general relativity with quantum theory. The resulting theory is called "quantum gravity" and is needed to better understand the origin of the universe, the nature of space and time on small scales, and what happens inside black holes. The research supported by this award will use the latest techniques and tools to try to study quantum fluctuations and their effects, especially rare but large spontaneous fluctuations of energy density. These are subtle effects which are not well understood. The results of this research may have applications to other areas of science and possibly to technology. The large fluctuations to be studied may play a role in nonlinear optics and quantum tunneling, two areas which have broad applications. The project will also have educational benefits. Students will participate in the research and gain valuable experience from doing so. The project should also produce examples which can be used to explain some of the concepts of quantum theory and relativity to students on a variety of educational levels.The project will investigate the probability distributions for quantum stress tensor fluctuations and their applications to gravity theory and other areas of physics. Particular attention will be paid to the asymptotic form of the distribution which governs the probability for large fluctuations. One approach to be used is the calculation of the large moments of the distribution. Preliminary studies indicate that this asymptotic form falls rather slowly compared to that for a thermal distribution. This indicates that quantum vacuum effects could dominate over thermal effects for large fluctuations, and suggests that new physical effects might be discovered in this line of research. Several models will be examined to look for such effects. One will be the effects of radiation pressure fluctuations on quantum tunneling of electrons and other particles. Another model will examine the effects of electric field fluctuations on the propagation of light in a nonlinear material. This study is of interest both for optical physics, and as an analog model for the quantum lightcone fluctuations expected in a quantum theory of gravity. The project will also examine the role of quantum stress tensor fluctuations in the early universe, especially in inflationary models.