Numerical Simulations for Quantum Cosmology

空间均匀的量子力学 宇宙学模型是重要的， 量子引力作为研究量子力学的竞技场 早期宇宙的影响。 的波函数 宇宙既可以作为 Wheeler-DeWitt方程或路径积分公式。 对于两个或三个以上的自由度， 可以使用解析差分法或数值差分法。 博士 Berger将应用几种数值模拟方法， 在许多情况下产生波函数（例如对于多电子 流体中的原子、凝聚态物质和溶解电子 具有任意数量自由度的系统）， 量子化宇宙模型 模拟的物理行为将被检查 特别是关于通货膨胀的存在， 波动和奇点避免。 正式问题将 用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.