Dispersive Quantum Systems

A dispersive quantum system is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of dispersive quantum systems within the class of completely positive Markovian quantum systems in finite dimension (through a homogeneous linear equation for the non-Hamiltonian part of the system’s Liouvillian). To set the framework, the basic features of quantum mechanics are reviewed focusing on time evolution and also on the theory of completely positive Markovian quantum systems, including Kossakowski–Lindblad’s standard form for Liouvillians. After those general considerations, a simple two-dimensional example is presented and then applied to describe the neutrino oscillation, with the introduction of a new “dispersive parameter.”