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Realistic many-body quantum systems vs full random matrices: static and dynamical properties

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems.