Neutral kaons as an open quantum system in a second quantization approach

TL;DR

This paper develops a quantum open system framework to describe the $CP$-violating evolution of decaying neutral kaons, providing explicit solutions and analyzing observable differences from $CP$-conserving cases.

Contribution

It introduces a second quantization approach to model $CP$ violation in open quantum systems, solving the Kossakowski-Lindblad equation explicitly for such particles.

Findings

Explicit solutions for $CP$-violating kaon evolution.

Calculation of observable differences from $CP$-conservation.

Framework unifies decay and flavor oscillations in open quantum systems.

Abstract

We have shown that it is possible to formulate the consistent and probability-preserving description of the $CP$-symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavour oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated $CP$ symmetry and found the evolution of _any_ observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the $CP$-preserved values.