Condensation and evolution of space-time network
  In this work, we try to propose, in a novel way using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of space time network described by the Loop quantum gravity. Considering quantum network connectivity features in the Loop quantum gravity, we introduce a link operator, and through extending the dynamical equation for the evolution of quantum network posed by Ginestra Bianconi to an operator equation, we get the solution of the link operator. This solution is relevant to the Hamiltonian of the network, and then is related to the energy distribution of network nodes. Showing that tremendous energy distribution induce huge curved space-time network, may have space time condensation in high-energy nodes. For example, in the black hole circumstances, quantum energy distribution is related to the area, thus the eigenvalues of the link operator of the nodes can be related to quantum number of area, and the eigenvectors are just the spin network states. This reveals that the degree distribution of nodes for space-time network is quantized, which can form the space-time network condensation. The black hole is a sort of result of space-time network condensation, however there may be more extensive space-time network condensation, for example, the universe singularity (big bang). 
Bi Qiao