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In most realistic models for quantum chaotic systems, the Hamiltonianmatrices in unperturbed bases have a sparse structure. We study correlations ineigenfunctions of such systems and derive explicit expressions for some of thecorrelation functions with respect to energy. The analytical results are testedin several models by numerical simulations. An application is given for arelation between transition probabilities.

Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices