Quantum chaos in a schematic shell model

To test the connection between chaotic classical motion and quantum spectral and overlap statistics, we examine a schematic three-orbital shell model. This system is novel in that the quantum phase space is compact and the momentum dependence of the classical Hamiltonian is nonstandard. We find good agreement with the expected behavior of the spectral statistics and reasonable agreement for the overlap distributions. Also, there is evidence that the eigenvector statistics are more sensitive to the details of the classical dynamics than are the eigenvalues.