Random matrix ensembles for semi-separable systems

Many models for chaotic systems consist of joining two integrable systems w ith incompatible constants of motion. The quantum counterparts of uch model s have a propagator which factorizes into two integrable parts. Each part c an be diagonalized. The two eigenvector bases are related by an orthogonal (or unitary) transformation. We construct a random matrix ensemble that mim ics this situation and consists of a product of a diagonal, an orthogonal, another diagonal and the transposed orthogonal matrix. The diagonal phases are chosen at random and the orthogonal matrix from Haar's measure. We deri ve asymptotic results (dimension N --> infinity) using Wick contractions. A new approximation for the group integration yields the next order in 1/N. We obtain a finite correction to the circular orthogonal ensemble, importan t in the long-range part of spectral correlations.