Fock state probability changes in open quantum systems

TL;DR

This paper introduces a path integral-based method to analyze how Fock state probabilities evolve in open quantum systems, demonstrated through a scalar field model and a neutrino toy model, revealing environmental effects on particle states.

Contribution

It presents a novel application of path integral techniques to directly compute Fock state probability changes in open quantum systems, bypassing complex master equation solutions.

Findings

Lighter neutrino masses cause greater environmental distortion of particle counts.

The method effectively models Fock state probability dynamics in scalar quantum field interactions.

Environmental interactions significantly influence particle state probabilities over time.

Abstract

Open quantum systems are powerful effective descriptions of quantum systems interacting with their environments. Studying changes of Fock state probabilities can be intricate in this context since the prevailing description of open quantum dynamics is by master equations of the systems' reduced density matrices, which usually requires finding solutions for a set of complicated coupled differential equations. In this article, we show that such problems can be circumvented by employing a recently developed path integral-based method for directly computing reduced density matrices in scalar quantum field theory. For this purpose, we consider a real scalar field $\phi$ as an open system interacting via a $\lambda \chi^2\phi^2$-term with an environment comprising another real scalar field $\chi$ that has a finite temperature. In particular, we investigate how the probabilities for observing the vacuum or two-particle states change over time if there were initial correlations of these Fock states. Subsequently, we apply our resulting expressions to a neutrino toy model. We show that, within our model, lighter neutrino masses would lead to a stronger distortion of the observable number of particles due to the interaction with the environment after the initial production process.