标题： 复量子网络在维度$d>2$中是无标度的 显示英文标题

标题： Complex Quantum Network Manifolds in Dimension $d>2$ are Scale-Free

摘要： 在量子引力中，迄今为止已经提出了几种用于离散几何量子描述的方法。这些理论框架包括圈量子引力、因果动态三角化、因果集、量子图性和能动自旋网络。这些方法中的大多数将离散空间描述为均匀的网络流形。在这里，我们定义了复杂数量网络流形（CQNM），它描述了量子网络状态的演化，并由维度为$d$的增长单纯复形构造而成。我们展示了在$d=2$中，CQNM 是均匀网络，而在$d>2$中，它们是无标度网络，即它们表现出像大多数复杂网络那样的大程度不均匀性。从 CQNM 的自组织演化中，量子统计自发出现。在这里，我们定义与$d$维度 CQNM 的$\delta$-面相关联的一般化度，并且我们展示了这些一般化度的统计特性可以根据$\delta$-面的维度遵循费米-狄拉克、玻尔兹曼或玻色-爱因斯坦分布。 显示英文摘要

摘要： In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension $d$. We show that in $d=2$ CQNM are homogeneous networks while for $d>2$ they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the $\delta$-faces of the $d$-dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the $\delta$-faces.