Quantum Dynamics

Abstract

In this chapter, dynamic properties of quantum networks will be addressed. We start with a discussion of closed systems. Principles of the dynamics of state vectors, density matrices, coherence vectors, and expectation values are studied, and the fundamental equations of motion (Schrödinger’s equation, Liouville’s equation, and Heisenberg’s equation of motion) are considered. As a fundamental example, the optically driven 2-level system is treated in detail leading to Bloch equations without damping. Coupled sets of Bloch equations describing 2- and 3-node functions are then introduced. Such coupled equations allow the discussion of systems composed of a number of subsystems (“nodes”). Finally, dynamic aspects of open systems under the influence of their respective surroundings are considered. A special master equation, the Markovian master equation, will be introduced. This will enable us to discuss damping models for 2- and 3-level systems, as well as to introduce generalized network equations with local damping.