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Ergodic transition on disordered random regular graph
Vladimir Kravtsov (ICTP, Trieste, Italy)
We consider statistics of eigenfunctions on the random regular graph with on-site disorder. The results of numerical diagonalization show a transition in the statistics of eigenfunctions deeply inside the region of extended states that is interpreted as a transition from extended ergodic to extended non-ergodic (multifractal) states. A comparison with the Rosenzweig-Porter random matrix theory and a generalized population dynamics calculations is discussed.