M. Kus et al., LEVEL DYNAMICS FOR CONSERVATIVE AND DISSIPATIVE QUANTUM-SYSTEMS, Journal of physics. A, mathematical and general, 30(24), 1997, pp. 8635-8651
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.