论文标题
马尔可夫链蒙特卡洛方法用于Spinfoam宇宙学中的图形细化方法
Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
论文作者
论文摘要
我们研究了洛伦兹（Lorentzian Engle-Pereira-Rovelli-rovelli-rivelli-rivelli-rivelli spinfoam振幅）的行为，并在五到二十个边界四面体的图形细化下具有均匀边界数据。这可以解释为宇宙的波函数，为此我们计算边界几何算子，相关函数和纠缠熵。通过适应大都市杂货算法以及最近开发的适合深量子制度的计算方法，使数值计算成为可能。我们确认过渡幅度在这种改进方面是稳定的。我们发现平均边界几何形状不会改变，但是新的自由度纠正了边界的量子波动和空间斑块之间的相关性。期望值与它们的几何解释兼容，并且在跨不同的Spinfoam顶点计算时相邻斑块衰减之间的相关性。
We study the behaviour of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph refinement going from five to twenty boundary tetrahedra. This can be interpreted as a wave function of the universe, for which we compute boundary geometrical operators, correlation functions and entanglement entropy. The numerical calculation is made possible by adapting the Metropolis-Hastings algorithm, along with recently developed computational methods appropriate for the deep quantum regime. We confirm that the transition amplitudes are stable against such refinement. We find that the average boundary geometry does not change, but the new degrees of freedom correct the quantum fluctuations of the boundary and the correlations between spatial patches. The expectation values are compatible with their geometrical interpretation and the correlations between neighbouring patches decay when computed across different spinfoam vertices.
