Quantum corrections to the geodesic equation

In this talk we will argue that, when gravitons are taken into account, the solution to the semiclassical Einstein equations (SEE) is not physical. The reason is simple: any classical device used to measure the spacetime geometry will also feel the graviton fluctuations. As the coupling between the classical device and the metric is non linear, the device will not measure the `background geometry' (i.e. the geometry that solves the SEE). As a particular example we will show that a classical particle does not follow a geodesic of the background metric. Instead its motion is determined by a quantum corrected geodesic equation that takes into account its coupling to the gravitons. This analysis will also lead us to find a solution to the so-called gauge fixing problem: the quantum corrected geodesic equation is explicitly independent of any gauge fixing parameter.Comment: Revtex file, 6 pages, no figures. Talk presented at the meeting "Trends in Theoretical Physics II", Buenos Aires, Argentina, December 199

Survival of quantum effects for observables after decoherence

When a quantum nonlinear system is linearly coupled to an infinite bath of harmonic oscillators, quantum coherence of the system is lost on a decoherence time-scale $\tau_D$. Nevertheless, quantum effects for observables may still survive environment-induced decoherence, and be observed for times much larger than the decoherence time-scale. In particular, we show that the Ehrenfest time, which characterizes a departure of quantum dynamics for observables from the corresponding classical dynamics, can be observed for a quasi-classical nonlinear oscillator for times $\tau \gg\tau_D$. We discuss this observation in relation to recent experiments on quantum nonlinear systems in the quasi-classical region of parameters.Comment: submitted to PR