Numerical Simulations for Quantum Cosmology (Physics)

空间齐次宇宙学模型的量子力学无论是作为量子引力的范例还是作为研究早期宇宙量子效应的舞台都是重要的。宇宙的波函数既可以作为Wheeler-DeWitt方程的解得到，也可以从路径积分公式中得到。对于两个或三个以上的自由度，既不能使用解析差分法，也不能使用数值差分法。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，对于具有任意自由度的流体系统中的多电子原子、凝聚态物质和溶解电子)产生波函数，以量化宇宙学模型。模拟的物理行为将被检查，特别是关于充气、波动和奇点避免的存在。正式的问题将以量子引力的晶格模拟作为最终目标。

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.