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

Thomas Guhr; Thomas Papenbrock

doi:10.1103/physreve.59.330

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

Thomas Guhr·Thomas Papenbrock

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Abstract

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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Thomas Guhr, Thomas Papenbrock. 1998-07-20. Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary Ensemble. https://doi.org/10.1103/physreve.59.330

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