# The Fermi problem in disordered systems

## TL;DR

This paper investigates how disorder in a medium affects causality and energy transfer between two quantum systems, revealing that classical causality emerges only in the wave zone amidst light cone fluctuations.

## Contribution

It introduces a model of disordered media with random Klein-Gordon coefficients to analyze causality and energy transfer in a quantum two-qubits system.

## Key findings

- Causality emerges only in the wave zone with disorder.
- Disorder causes fluctuations in the light cone.
- Energy transfer dynamics are affected by medium randomness.

## Abstract

We revisit the Fermi two-atoms problem in the framework of disordered systems. In our model we consider a two-qubits system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.