# Fock state probability changes in open quantum systems

## TL;DR

This paper introduces a new method to study how probabilities of quantum states change in systems interacting with their environment, avoiding complex differential equations.

## Contribution

A path integral-based method is used to compute reduced density matrices in open quantum systems, bypassing traditional master equations.

## Key findings

- The method allows direct computation of Fock state probability changes in scalar quantum field theory.
- Initial correlations in vacuum or two-particle states significantly affect their time evolution.
- Lighter neutrino masses cause stronger particle number distortions due to environmental interactions.

## 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 \documentclass[12pt]{minimal}
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\begin{document}$$\lambda \chi ^2\phi ^2$$\end{document}λχ2ϕ2-term with an environment comprising another real scalar field \documentclass[12pt]{minimal}
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\begin{document}$$\chi $$\end{document}χ 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.