Dynamics of open quantum systems

Abstract

This chapter provides a brief introduction to quantum systems that are coupled to large reservoirs. It aims to remind the reader of well-known concepts necessary for the understanding of the book and does not claim to provide a selfcontained introduction. It starts with a brief summary of the conventions used in the book and then introduces master equations with some examples. This also requires us to introduce the density matrix: among other things, we discuss its evolution in a closed system and under measurements. To connect to system-reservoir theories, we also review the definition of the tensor product and the partial trace. Finally, we introduce the Lindblad form of a quantum master equation and discuss its properties before closing with some remarks on the superoperator representation of master equations.