Numerical Simulations for Quantum Cosmology

量子宇宙学的数值模拟

• 批准号: 9107162
• 负责人: Beverly Berger
• 金额: $ 3.95万
• 依托单位: Oakland University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107162&HistoricalAwards=false
• 关键词: Numerical; Simulations; Quantum; Cosmology

The quantum mechanics of spatially homogenous cosmological models is important both as a paradigm for quantum gravity and as an arena for the study of quantum effects in the Early Universe. The wave function of the Universe may be obtained either as the solution to the Wheeler-DeWitt equation or from a path integral formulation. For more than two or three degrees of freedom, neither analytic nor numerical differencing methods can be used. Dr. Berger will apply several numerical simulation methods which yield wave functions in many contexts (e.g. for multi-electron atoms, condensed matter, and dissolved electron in fluid systems with an arbitrary number of degrees of freedom) to quantized cosmological models. The physical behavior of the simulations will be examined particularly with regard to the presence of inflation, fluctuations, and singularity avoidance. Formal issues will be pursued with a lattice simulation of quantum gravity as the eventual goal.

空间同质宇宙学模型的量子力学作为量子引力的范式和早期宇宙中量子效应研究的舞台是重要的。宇宙的波函数可以作为惠勒-德维特方程的解或从路径积分公式中得到。对于两个或三个以上的自由度，既不能使用解析方法，也不能使用数值差分方法。Berger博士将应用几种数值模拟方法，这些方法在许多情况下（例如，对于具有任意数量自由度的多电子原子，凝聚态物质和溶解电子的流体系统）产生波函数，以量子化宇宙学模型。模拟的物理行为将特别考虑到膨胀、波动和奇点回避的存在。正式问题将以量子引力的晶格模拟作为最终目标进行探讨。