Abstract
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 is instability possible in a quantum system having finite ${d}_{\mathrm{H}}$?
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
