Exact description of spectral correlators by a quantum one-dimensional model with inverse-square interaction

The universal correlations which describe the response of energy levels of a disordered metallic grain to an arbitrary perturbation are shown to be equivalent to time-dependent correlations of a one-dimensional quantum Hamiltonian with inverse-square interaction. These resutls establish a direct connection between a strongly interacting quantum Hamiltonian, the nonlinear {σ} model of disordered electronic systems, and quantum chaotic spectra. As a consequence we have an expression for the correlation function of the quantum Hamiltonian which we believe to be exact for all space and time.