Metric fluctuations and decoherence

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.Comment: 7 page

Space--time fluctuations and the spreading of wavepackets

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.Comment: 11 page

Metric fluctuations and the Weak Equivalence Principle

We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging procedure over a finite space--time scale given by the quantum particle in the non--relativistic limit a modified Schr\"odinger equation. The dominant modification consists in an anomalous inertial mass tensor which depends on the type of particle and on the fluctuation scenario. The scenario considered in this paper is a most simple picture of spacetime fluctuations and gives an existence proof for an apparent violation of the weak equivalence principle and, in general, for a violation of Lorentz invariance.Comment: 10 pages, to appear in Class. Quantum Grav. (2008

Energy eigenfunctions of the 1D Gross-Pitaevskii equation

We developed a new and powerful algorithm by which numerical solutions for excited states in a gravito optical surface trap have been obtained. They represent solutions in the regime of strong nonlinearities of the Gross--Pitaevskii equation. In this context we also shortly review several approaches which allow, in principle, for calculating excited state solutions. It turns out that without modifications these are not applicable to strongly nonlinear Gross-Pitaevskii equations. The importance of studying excited states of Bose-Einstein condensates is also underlined by a recent experiment of B\"ucker et al in which vibrational state inversion of a Bose-Einstein condensate has been achieved by transferring the entire population of the condensate to the first excited state. Here, we focus on demonstrating the applicability of our algorithm for three different potentials by means of numerical results for the energy eigenstates and eigenvalues of the 1D Grosss-Pitaevskii-equation. We compare the numerically found solutions and find out that they completely agree with the case of known analytical solutions.Comment: 18 pages, 11 figure

Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) - A class-M fundamental physics mission proposal for Cosmic Vision 2015-2025: 2010 Update

This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper [Experimental Astronomy 23 (2009) 491-527; designated as Paper I] which was based on our last proposal submitted for the 2007 ESA call. In this paper, we present our orbit selection with one Venus swing-by together with orbit simulation. In Paper I, our orbit choice is with two Venus swing-bys. The present choice takes shorter time (about 250 days) to reach the opposite side of the Sun. We also present a preliminary design of the optical bench, and elaborate on the solar physics goals with the radiation monitor payload. We discuss telescope size, trade-offs of drag-free sensitivities, thermal issues and present an outlook. ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals.Comment: 15 pages, 11 figures, 1 table, based on our 2010 proposal submitted for the ESA call for class-M mission proposals, a sequel and an update to previous paper [Experimental Astronomy 23 (2009) 491-527] which was based on our last proposal submitted for the 2007 ESA call, submitted to Experimental Astronom