  We study the dynamics of a quantum system having Hilbert space of finite
dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master
equation governing the system's dynamics contain nonlinear terms. Here we
consider the nonlinear master equation derived by Grabert. The dynamics near a
fixed point is analyzed by using the method of linearization, and by evaluating
the eigenvalues of the Jacobian matrix. We find that all these eigenvalues are
non-negative, and conclude that the fixed point is stable. This finding raises
the question: under what conditions instability is possible in a quantum system
having finite $d_{\mathrm{H}}$?
