Metric fluctuations and decoherence

TL;DR

This paper explores how metric fluctuations induce decoherence in quantum particles, leading to energy localization and providing a detailed quantum master equation analysis of the decoherence process.

Contribution

It introduces a model where metric fluctuations cause decoherence and derives a master equation showing energy-space localization effects.

Findings

Metric fluctuations cause decoherence of quantum particles.

Decoherence leads to localization in energy space.

Decoherence time scales are estimated.

Abstract

Recently a model of metric fluctuations has been proposed which yields an effective Schr\"odinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization of the inertial mass tensor results from a local space average over the fluctuations of the metric over a fixed background metric. Here, we demonstrate that the metric fluctuations of this model lead to a further physical effect, namely to an effective decoherence of the quantum particle. We derive a quantum master equation for the particle's density matrix, discuss in detail its dissipation and decoherence properties, and estimate the corresponding decoherence time scales. By contrast to other models discussed in the literature, in the present approach the metric fluctuations give rise to a decay of the coherences in the energy representation, i. e., to a localization in energy space.