Derivation of Markovian master equation by renormalization group method

TL;DR

This paper derives the Markovian master equation using the renormalization group method, starting from the von Neumann equation and assuming short bath correlation times, resulting in the GKLS form in the weak coupling limit.

Contribution

It introduces a novel derivation of the Markovian master equation via the renormalization group approach, clarifying the removal of initial time dependence.

Findings

Derivation of the GKLS form of the master equation

Application of the renormalization group method to open quantum systems

Demonstration of the weak coupling limit validity

Abstract

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.