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In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations. An application is given for a relation between transition probabilities.
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of states viol
The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of the reduce
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices is valid
The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of black-hole entr
We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements.