Dissipation and decoherence in quantum systems

Abstract

These lecture notes address an audience of physicists or mathematicians whohave been exposed to a first course in quantum mechanics. We start with a briefdiscussion of the general "system-bath" paradigm of quantum dissipativesystems, analyze in some detail the simplest example of "pure dephasing" of atwo-level system, and review the basic concept of the density matrix. We thentreat the general dissipative time-evolution, introducing completely positivemaps, their relation to entanglement theory, and their Kraus decomposition.Restricting ourselves to Markovian evolution, we discuss the Lindblad form ofmaster equations. The notes conclude with an overview of topics of currentinterest that go beyond Lindblad Markov master equations. (These notes wereprepared for lectures delivered by F. Marquardt in October 2007 at the Langeoogworkshop of the SFB/TR 12, "Symmetries and Universality in Mesoscopic Systems")