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- W2059310048 abstract "We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential Tr W(H), we (i) find the joint distribution functions of the eigenvalues of H and H' = H + V for an arbitrary fixed V both for finite matrix size N and in the 'thermodynamic' N → ∞ limit; (ii) derive many-point parametric correlation functions of the two sets of eigenvalues and show that they are naturally parametrized by the eigenvalues of the reactance matrix for scattering off the 'potential' V; (iii) prove the universality of the correlation functions in unitary ensembles with non-Gaussian non-invariant confinement potential Tr W(H − V); (iv) establish a general scheme for exact calculation of level-number-dependent parametric correlation functions and apply the scheme to the calculation of intra-level velocity autocorrelation function and the distribution of parametric level shifts." @default.
- W2059310048 created "2016-06-24" @default.
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- W2059310048 date "2003-03-13" @default.
- W2059310048 modified "2023-09-26" @default.
- W2059310048 title "Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations" @default.
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- W2059310048 doi "https://doi.org/10.1088/0305-4470/36/12/339" @default.
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