Field theoretical approach to open quantum systems and the Lindblad equation

Hans C. Fogedby

Published 2022-02-10Version 1

We develop a field theoretical approach to open quantum systems based on condensed matter many body methods. The time evolution of the reduced density matrix for the open system is determined by a transmission matrix. Invoking Wick's theorem in connection with a Caldeira-Leggett quantum oscillator environment the transmission matrix satisfies a Dyson equation characterised by an irreducible kernel. The Dyson equation is equivalent to a general master equation for the reduced density matrix. We consider the Born approximation for the kernel. Applying a condensed matter "quasi-particle-type" approximation we obtain a Master equation of the Markov type. Imposing the rotating wave approximation we obtain a Markov master equation of the Lindblad form. As a standard example we discuss the case of a single qubit coupled to a thermal heat bath.