Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Spontaneous mechanical oscillation of a DC driven single crystal

There is a large interest to decrease the size of mechanical oscillators since this can lead to miniaturization of timing and frequency referencing devices, but also because of the potential of small mechanical oscillators as extremely sensitive sensors. Here we show that a single crystal silicon resonator structure spontaneously starts to oscillate when driven by a constant direct current (DC). The mechanical oscillation is sustained by an electrothermomechanical feedback effect in a nanobeam, which operates as a mechanical displacement amplifier. The displacement of the resonator mass is amplified, because it modulates the resistive heating power in the nanobeam via the piezoresistive effect, which results in a temperature variation that causes a thermal expansion feedback-force from the nanobeam on the resonator mass. This self-amplification effect can occur in almost any conducting material, but is particularly effective when the current density and mechanical stress are concentrated in beams of nano-scale dimensions

Estimation of a general parametric location in censored regression

In this study, we explore the pattern of efficiency among enterprises in China’s 29 provinces across different ownership types in heavy and light industries and across different regions (coastal, central and western). We do so by performing a bootstrap-based analysis of group efficiencies (weighted and non-weighted), estimating and comparing densities of efficiency distributions, and conducting a bootstrapped truncated regression analysis. We find evidence of interesting differences in efficiency levels among various ownership groups, especially for foreign and local ownership, which have different patterns for light and heavy industries