LEVEL DYNAMICS FOR CONSERVATIVE AND DISSIPATIVE QUANTUM-SYSTEMS

We establish level dynamics for finite matrices, employing a unified t reatment of real symmetric, complex Hermitian, quaternion real, unitar y, and arbitrary complex matrices. In all cases the level dynamics tak e the form of the classical Hamiltonian Bow of some fictitious many-pa rticle 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 arb itrary complex matrices.