English

Stability of the Grabert master equation

Quantum Physics 2021-06-02 v1

Abstract

We study the dynamics of a quantum system having Hilbert space of finite dimension dHd_{\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 dHd_{\mathrm{H}}?

Keywords

Cite

@article{arxiv.2103.08982,
  title  = {Stability of the Grabert master equation},
  author = {Eyal Buks and Dvir Schwartz},
  journal= {arXiv preprint arXiv:2103.08982},
  year   = {2021}
}
R2 v1 2026-06-24T00:13:53.030Z