Spacetime fluctuations and the spreading of wavepackets

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 Schrödinger 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.

Fluctuations of spacetime and holographic noise in atomic interferometry

“…We will show in the following that this Schrödinger equation leads to an apparent violation of the weak equivalence principle [20], to a modified dynamics of wavepackets [15] and to a decay of coherences in energy representation [21]. Sincer is constant over the averaging scale it just represents a constant shift of energy what can be omitted.…”

Quantum spacetime fluctuations: Lamb shift and hyperfine structure of the hydrogen atom

“…Indeed, γ is not equal to σ (γ ij in the general situation) [25,26]. They correspond to different statistical features of the involved fluctuations of spacetime.…”

“…We consider conformal fluctuations [25,26], namely, γ ij = 0, if i = j, whereas γ xx = γ yy = γ zz = γ. These conditions reduce (4) tô…”

“…The assumption of conformal fluctuations implies [25,26] that the average of this change (here denoted by < ∆V >)…”

“…In particular we will address the issue of the consequences of the presence of metric fluctuations [25,26] upon the properties of a hydrogen atom. The main ingredient in this aspect corresponds to a Minkowskian background and in addition small spacetime fluctuations are also present.…”