Statistical Mechanics in General Relativity and Gravitational Physics

本研究的目的是将统计力学、等离子体物理学，特别是动力系统理论中最新发展的思想和技术应用于涉及物体自引力系统演化的问题，包括牛顿和广义相对论。要考虑的一个一般问题是星系和星系核的“松弛”和稳定性。这里有两个主要目的：(a)从第一性原理理解观测到的星系间相似性的起源，这是一个重要的问题，因为名义弛豫时间tR通常比宇宙年龄大几个数量级；与此相关的是，(b)了解星系如何对强大的外部刺激作出反应，例如，通过与其他星系的碰撞，通过非常迅速地向新的统计平衡发展。另一个需要考虑的领域涉及到早期宇宙中从统计物理学到量子场论的应用。这里有两个主要目标：(a)将相变和其他量子场论过程建模为简单的随机过程；(b)分析早期宇宙中的粒子产生，最终目的是提高对“引力熵”和观察到的“时间之箭”的理解。

The objective of this research is to apply recently developed ideas and techniques from statistical mechanics, plasma physics, and, particularly, dynamical systems theory to problems involving the evolution of self-gravitating systems of objects, both Newtonianly and in general relativity. One general problem to be considered is the "relaxation" and stability of galaxies and galactic nuclei. Two principal aims here are (a) to understand from first principles the origins of the observed similarities amongst galaxies, a nontrivial issue in that the nominal relaxation time tR is typically orders of magnitude larger than the age of the Universe; and related to this, (b) to understand how galaxies respond to strong external stimuli, as provided, e.g., by collisions with other galaxies, by very rapidly evolving towards a new statistical equilibrium. The other area to be considered entails an application of ideas from statistical physics to quantum field theory in the early Universe. Two principal aims here are (a) the modeling of phase transitions and other quantum field theoretic processes as simple stochastic processes and (b) an analysis of particle creation in the early Universe, with the ultimate aim of obtaining an improved understanding of "gravitational entropy" and the observed "arrow of time."