# Space--time fluctuations and the spreading of wavepackets

## TL;DR

This paper investigates how classical space-time fluctuations influence wavepacket evolution by deriving a master equation from a fluctuating metric, revealing their impact on wavepacket diffusion.

## Contribution

It introduces a novel approach to model wavepacket dynamics in fluctuating space-time using a master equation derived from a non-minimally coupled Klein-Gordon framework.

## Key findings

- Space-time fluctuations modify wavepacket diffusion properties.
- Different fluctuation scenarios lead to distinct diffusion behaviors.
- The derived master equation effectively describes wavepacket evolution in fluctuating backgrounds.

## Abstract

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein-Gordon equation we derive a Schr\"odinger equation with an additive gaussian random potential. This is transformed into an effective master equation for the density matrix. The solutions of this master equation allow to study the dynamics of wavepackets in a fluctuating space-time, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.