Stability of the Grabert master equation
- Resource Type
- Working Paper
- Authors
- Buks, Eyal; Schwartz, Dvir
- Source
- Phys. Rev. A 103, 052217 (2021)
- Subject
- Quantum Physics
- Language
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 $d_{\mathrm{H}}$?