  We consider a system of linear oscillators, or quantum states, described by
Random Matrix Theory and analyze how its time evolution is affected by a
nonlinear perturbation. Our numerical results show that above a certain chaos
border a weak or moderate nonlinearity leads to a dynamical thermalization of a
finite number of degrees of freedom with energy equipartition over linear
eigenmodes as expected from the laws of classical statistical mechanics. The
system temperature is shown to change in a broad range from positive to
negative values and the dependence of system characteristics on the initial
injected energy is determined. Below the chaos border the dynamics is described
by the Kolmogorov-Arnold-Moser integrability. Due to universal features of
Random Matrix Theory we argue that the obtained results describe the generic
properties of its nonlinear perturbation.
