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Springer eBooks

The Matrix Perturbation Method for the Lindblad Master Equation

Francisco Soto, Braulio Misael Villegas-Martínez, H. M. Moya-Cessa

Published Jan 1, 2023• 0 citations
Publisher
DOI
10.1007/978-3-031-48546-6_6

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The Matrix Perturbation Method

Francisco Soto, Braulio Misael Villegas-Martínez, H. M. Moya-Cessa

Springer eBooks•Jan 1, 2023•0 citations
We present a derivation of the Markovian master equation by the renormalization group method. Starting from a naive perturbative solution of the von Neumann equation, the reduced density matrix with the coarse grained time steps is obtained using the assumption of short correlation time of the bath field. Then by applying the renormalization group method, we show that the dependence of the specific initial time on the perturbative solution can be removed and the Markovian semigroup master equation in the Gorini--Kossakowski--Lindblad--Sudarshan (GKLS) form is obtained in the weak coupling limit.
We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating the Q -function, the average number of photons, and the distance between density matrices.