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

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.