Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary Ensemble

Details Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary Ensemble Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary Ensemble

1998-07-20

arxiv.org/abs/chao-dyn/9807028v1

Phys. Rev. E 59 (1999) 330

Nonlinear Sciences

Chaotic Dynamics

12 pages, 4 EPS-figures, uses psfig.sty

Scientific paper

10.1103/PhysRevE.59.330

We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In contrast to certain related transitions, the k-point correlation function possesses the k*k determinant structure of the GUE limit for the entire transition. The results are used to consider also the spectral correlations of a superposition of M transition spectra. Our results are non-perturbative and are valid for all values of the transition parameter.

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