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 har monic oscillator towards the Gaussian unitary ensemble (GUE). We use a vari ant of the supersymmetry method to obtain analytical results in a fast and elegant way. In contrast to certain related transitions, the k-point correl ation function possesses the kxk 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 no nperturbative and are valid for all values of the transition parameter. [S1 063-651X(99)01801-2].