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arXiv:2002.00410 · The European Physical Journal Plus

A perturbation algorithm for the pointers of Franke–Gorini–Kossakowski–Lindblad–Sudarshan equation

Alexander A. Andrianov, M. V. Ioffe, Ekaterina Izotova, Oleg O. Novikov

Published Jun 1, 2020• 3 citations
arXivHTMLPDF
DOI
10.1140/epjp/s13360-020-00540-3

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Abstract We present an alternative derivation of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation based on complex Riccati equations and the associated dynamical invariants. Our formulation introduces time-dependent coefficients, which satisfy the constraints imposed by the Robertson-Schrödinger uncertainty relations, as previously discussed by Dekker et al. in the time-independent case. This time dependence may provide new insights and perspectives for extending the framework to non-Markovian systems.
An open quantum system can be described by a master equation, of which one of the most popular is the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We revisit description of driven-dissipative quantum systems focusing on the appropriate choice of the system's basis and the respective transformations. We consider the GKSL equation in different bases and calculate the dynamics for a qubit and for a qudit. An appropriate choice of the basis is a fundamental problem for theoretical consideration of open quantum systems and provides an opportunity to obtain the desired evolution in practice.