Eigenvalue tunnelling and decay of quenched random networkстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 6 февраля 2017 г.
Аннотация:We consider the canonical ensemble of N-vertex Erd\H{o}s-R\'enyi (ER) random topological graphs with quenched vertex degree, and with fugacity \mu for each closed triple of bonds. We claim complete defragmentation of large-N graphs into the collection of [p-1] almost full subgraphs (cliques) above critical fugacity, \mu_c, where p is the ER bond formation probability. Evolution of the spectral density, \rho(\lambda), of the adjacency matrix with increasing \mu leads to the formation of a multi-zonal support for \mu>\mu_c. Eigenvalue tunnelling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuate around the mean value Np. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.