Energy-level statistics for a relaxation Hamiltonian

We report a numerical computation of the energy-level spacing distribution, the spectral rigidity, and the transition-amplitude distribution for an ensemble of Hamiltonians with a single ‘‘bright’’ state interacting with a manifold of ‘‘bath’’ states. The bath states are assumed to be part of a regular spectrum so that the initial states have Poisson statistics. Despite very strong average coupling of all bath states to the bright state (which may represent coupling to another electronic surface), statistical properties of the final spectrum are more like those of the initial bath distribution than those of the Gaussian orthogonal ensemble distribution expected for an irregular quantum spectrum. The level spacings show level repulsion, but with the nonlinear threshold behavior P(s)∼$s^{0.625}$.