Level dynamics for conservative and dissipative quantum systems

We establish level dynamics for finite matrices, employing a unified treatment of real symmetric, complex Hermitian, quaternion real, unitary, and arbitrary complex matrices. In all cases the level dynamics take the form of the classical Hamiltonian Bow of some fictitious many-particle systems. Equilibrium statistical mechanics of the latter leads to the well known matrix ensembles of random-matrix theory. Ginibre's ensemble, in particular, is thus associated with level dynamics of arbitrary complex matrices.