Spacetime fluctuations and the spreading of wavepackets

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating spacetime background. We assume that spacetime fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein-Gordon equation, we derive a Schrodinger 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 us to study the dynamics of wavepackets in a fluctuating spacetime, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.