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arXiv · 2103.08982

Stability of the Grabert master equation

Eyal Buks·Dvir Schwartz
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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 instability is possible in a quantum system having finite $d_{\mathrm{H}}$?

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Eyal Buks, Dvir Schwartz. 2021-03-16. Stability of the Grabert master equation. https://doi.org/10.1103/physreva.103.052217

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