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Parametric spectral correlations in disordered and chaotic structures

I. E. Smolyarenko·F. M. Marchetti·B. D. Simons
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Abstract

We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the (n,m)-point parametric correlation function of the initial and final density of states for perturbations of arbitrary rank and strength. A further generalization of these results allows for the incorporation of short-range spatial correlations in diffusive as well as ballistic chaotic structures.

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I. E. Smolyarenko, F. M. Marchetti, B. D. Simons. 2002-07-18. Parametric spectral correlations in disordered and chaotic structures. https://doi.org/10.1103/physrevlett.88.256808

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