Master-Equation Formulations of Decoherence

Abstract

In this chapter, we will introduce the description of decoherence dynamics in terms of so-called master equations. Such master equations directly and conveniently yield the time evolution of the reduced density matrix ˆρ_S(t) for the open quantum system S interacting with an environment E. They relieve us from the need of having to first determine the dynamics of the total system–environment combination and to then trace out the degrees of freedom of the environment. The master-equation approach is motivated by two issues. First, we are usually not interested in the dynamics of the environment or of the global system–environment combination. All we really care about is the influence of the environment on our system of interest. Second, it is often impossible to analytically determine the time evolution of the density matrix. In such cases, one can use approximation schemes that lead to master equations for the approximate evolution of the reduced density matrix.