Gravity tests in the solar system and the Pioneer anomaly

We build up a new phenomenological framework associated with a minimal generalization of Einsteinian gravitation theory. When linearity, stationarity and isotropy are assumed, tests in the solar system are characterized by two potentials which generalize respectively the Newton potential and the parameter $\gamma$ of parametrized post-Newtonian formalism. The new framework seems to have the capability to account for the Pioneer anomaly besides other gravity tests.Comment: 5 pages. Accepted version, to appear in Modern Physics Letters

Test of Guttmann and Enting's conjecture in the eight-vertex model

We investigate the analyticity property of the partially resummed series expansion(PRSE) of the partition function for the eight-vertex model. Developing a graphical technique, we have obtained a first few terms of the PRSE and found that these terms have a pole only at one point in the complex plane of the coupling constant. This result supports the conjecture proposed by Guttmann and Enting concerning the ``solvability'' in statistical mechanical lattice models.Comment: 15 pages, 3 figures, RevTe

Motion Induced Radiation from a Vibrating Cavity

We study the radiation emitted by a cavity moving in vacuum. We give a quantitative estimate of the photon production inside the cavity as well as of the photon flux radiated from the cavity. A resonance enhancement occurs not only when the cavity length is modulated but also for a global oscillation of the cavity. For a high finesse cavity the emitted radiation surpasses radiation from a single mirror by orders of magnitude.Comment: 4 pages, to appear in Physical Review Letter

Quantum Limits in Space-Time Measurements

Quantum fluctuations impose fundamental limits on measurement and space-time probing. Although using optimised probe fields can allow to push sensitivity in a position measurement beyond the "standard quantum limit", quantum fluctuations of the probe field still result in limitations which are determined by irreducible dissipation mechanisms. Fluctuation-dissipation relations in vacuum characterise the mechanical effects of radiation pressure vacuum fluctuations, which lead to an ultimate quantum noise for positions. For macroscopic reflectors, the quantum noise on positions is dominated by gravitational vacuum fluctuations, and takes a universal form deduced from quantum fluctuations of space-time curvatures in vacuum. These can be considered as ultimate space-time fluctuations, fixing ultimate quantum limits in space-time measurements.Comment: 11 pages, to appear in Quantum and Semiclassical Optic

Fluctuations of the Retarded Van der Waals Force

The retarded Van der Waals force between a polarizable particle and a perfectly conducting plate is re-examined. The expression for this force given by Casimir and Polder represents a mean force, but there are large fluctuations around this mean value on short time scales which are of the same order of magnitude as the mean force itself. However, these fluctuations occur on time scales which are typically of the order of the light travel time between the atom and the plate. As a consequence, they will not be observed in an experiment which measures the force averaged over a much longer time. In the large time limit, the magnitude of the mean squared velocity of a test particle due to this fluctuating Van der Waals force approaches a constant, and is similar to a Brownian motion of a test particle in an thermal bath with an effective temperature. However the fluctuations are not isotropic in this case, and the shift in the mean square velocity components can even be negative. We interpret this negative shift to correspond to a reduction in the velocity spread of a wavepacket. The force fluctuations discussed in this paper are special case of the more general problem of stress tensor fluctuations. These are of interest in a variety of areas fo physics, including gravity theory. Thus the effects of Van der Waals force fluctuations serve as a useful model for better understanding quantum effects in gravity theory.Comment: 14 pages, no figure

Constraints on f(RijklRijkl)f(R_{ijkl}R^{ijkl}) gravity: An evidence against the covariant resolution of the Pioneer anomaly

We consider corrections in the form of $\Delta L(R_{ijkl}R^{ijkl})$ to the Einstein-Hilbert Lagrangian. Then we compute the corrections to the Schwarszchild geometry due to the inclusion of this general term to the Lagrangian. We show that $\Delta L_3=\alpha_{{1/3}}(R_{ijkl}R^{ijkl})^{{1/3}}$ gives rise to a constant anomalous acceleration for objects orbiting the Sun onward the Sun. This leads to the conclusion that $\alpha_{{1/3}}=(13.91\pm 2.11) \times 10^{-26}(\frac{1}{\text{meters}})^{{2/3}}$ would have covariantly resolved the Pioneer anomaly if this value of $\alpha_{{1/3}}$ had not contradicted other observations. We notice that the experimental bounds on $\Delta L_3$ grows stronger in case we examine the deformation of the space-time geometry around objects lighter than the Sun. We therefore use the high precision measurements around the Earth (LAGEOS and LLR) and obtain a very strong constraint on the corrections in the form of $\Delta L(R_{ijkl}R^{ijkl})$ and in particular $\Delta L=\alpha_n(R_{ijkl}R^{ijkl})^n$. This bound requires $\alpha_{{1/3}}\leq6.12\times 10^{-29}(\frac{1}{\text{meters}})^{{2/3}}$. Therefore it refutes the covariant resolution of the Pioneer anomaly.Comment: ...v5: references added, new discussions adde

Vacuum fluctuations, accelerated motion and conformal frames

Radiation from a mirror moving in vacuum electromagnetic fields is shown to vanish in the case of a uniformly accelerated motion. Such motions are related to conformal coordinate transformations, which preserve correlation functions characteristic of vacuum fluctuations. As a result, vacuum fluctuations remain invariant under reflection upon a uniformly accelerated mirror, which therefore does not radiate and experiences no radiation reaction force. Mechanical effects of vacuum fluctuations thus exhibit an invariance with respect to uniformly accelerated motions.Comment: 7 page

Dynamical Casimir Effect in a Leaky Cavity at Finite Temperature

The phenomenon of particle creation within an almost resonantly vibrating cavity with losses is investigated for the example of a massless scalar field at finite temperature. A leaky cavity is designed via the insertion of a dispersive mirror into a larger ideal cavity (the reservoir). In the case of parametric resonance the rotating wave approximation allows for the construction of an effective Hamiltonian. The number of produced particles is then calculated using response theory as well as a non-perturbative approach. In addition we study the associated master equation and briefly discuss the effects of detuning. The exponential growth of the particle numbers and the strong enhancement at finite temperatures found earlier for ideal cavities turn out to be essentially preserved. The relevance of the results for experimental tests of quantum radiation via the dynamical Casimir effect is addressed. Furthermore the generalization to the electromagnetic field is outlined.Comment: 48 pages, 8 figures typos corrected & references added and update

Pioneer 10 Doppler data analysis: disentangling periodic and secular anomalies

This paper reports the results of an analysis of the Doppler tracking data of Pioneer probes which did show an anomalous behaviour. A software has been developed for the sake of performing a data analysis as independent as possible from that of J. Anderson et al. \citep{anderson}, using the same data set. A first output of this new analysis is a confirmation of the existence of a secular anomaly with an amplitude about 0.8 nms$^{-2}$ compatible with that reported by Anderson et al. A second output is the study of periodic variations of the anomaly, which we characterize as functions of the azimuthal angle $\varphi$ defined by the directions Sun-Earth Antenna and Sun-Pioneer. An improved fit is obtained with periodic variations written as the sum of a secular acceleration and two sinusoids of the angles $\varphi$ and $2\varphi$. The tests which have been performed for assessing the robustness of these results are presented.Comment: 13 pages, 6 figures, minor amendment

Radiation Pressure as a Source of Decoherence

We consider the interaction of an harmonic oscillator with the quantum field via radiation pressure. We show that a `Schrodinger cat' state decoheres in a time scale that depends on the degree of `classicality' of the state components, and which may be much shorter than the relaxation time scale associated to the dynamical Casimir effect. We also show that decoherence is a consequence of the entanglement between the quantum states of the oscillator and field two-photon states. With the help of the fluctuation-dissipation theorem, we derive a relation between decoherence and damping rates valid for arbitrary values of the temperature of the field. Coherent states are selected by the interaction as pointer states.Comment: 14 pages, 3 figures, RevTex fil