Abstract
The Caldeira-Leggett master equation as an example of Markovian master equation without Lindblad form is investigated for mathematical consistency. We explore situations both analytically and numerically where the positivity violations of the density operator occur. We reinforce some known knowledge about this problem but also find new surprising cases. Our analytical results are based on the full solution of the Caldeira-Leggett master equation obtained via the method of characteristics. The preservation of positivity is mainly investigated with the help of the density operator’s purity and we give also some numerical results about the violation of the Robertson-Schrödinger uncertainty relation.
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25 June 2019
This erratum corrects three mistakes. The first is a typo, the second one is an unclear statement about the states used in the numerical simulations, and the third is a misused reference with respect to an equation.
25 June 2019
This erratum corrects three mistakes. The first is a typo, the second one is an unclear statement about the states used in the numerical simulations, and the third is a misused reference with respect to an equation.
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Homa, G., Bernád, J.Z. & Lisztes, L. Positivity violations of the density operator in the Caldeira-Leggett master equation. Eur. Phys. J. D 73, 53 (2019). https://doi.org/10.1140/epjd/e2019-90604-4
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DOI: https://doi.org/10.1140/epjd/e2019-90604-4