Dispersive Quantum Systems: a class of isolated non-time reversal quantum systems

TL;DR

This paper introduces dispersive quantum systems, a class of isolated, non-time reversal invariant quantum systems, providing their formal definitions, characterizations, and an example related to neutrino oscillations.

Contribution

It defines dispersive quantum systems, characterizes them within finite-dimensional Markovian quantum systems, and illustrates their application to neutrino oscillation modeling.

Findings

Dispersive quantum systems are formally defined and characterized.

A simple two-level dispersive system example is provided.

Application to neutrino oscillation is demonstrated.

Abstract

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, I present a simple example of dispersive two-level quantum system and apply that to describe neutrino oscillation.