Parametric level correlations in random-matrix models

Weidenmüller, Hans A.

doi:10.1088/0953-8984/17/20/015

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Parametric level correlations in random-matrix models

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Weidenmüller, Hans A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Citation

Weidenmüller, H. A. (2005). Parametric level correlations in random-matrix models. Journal of Physics: Condensed Matter, 17(20), S1881-S1887. doi:10.1088/0953-8984/17/20/015.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-88F9-C

Abstract

We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle-point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications.