Recently a model of metric fluctuations has been proposed which yields an effective Schrodinger 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 particles 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.
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