Notes on moving mirrors

The Davies-Fulling (DF) model describes the scattering of a massless field by a non-inertial mirror in two dimensions. In this paper, we generalize this model in two different ways. First, we consider partially reflecting mirrors. We show that the Bogoliubov coefficients relating inertial modes can be expressed in terms of the frequency dependent reflection factor which is specified in the rest frame of the mirror and the transformation from the inertial modes to the modes at rest with respect to the mirror. In this perspective, the DF model is simply the limiting case when this factor is unity for all frequencies. In the second part, we introduce an alternative model which is based on self-interactions described by an action principle. When the coupling is constant, this model can be solved exactly and gives rise to a partially reflecting mirror. The usefulness of this dynamical model lies in the possibility of switching off the coupling between the mirror and the field. This allows to obtain regularized expressions for the fluxes in situations where they are singular when using the DF model. Two examples are considered. The first concerns the flux induced by the disappearance of the reflection condition, a situation which bears some analogies with the end of the evaporation of a black hole. The second case concerns the flux emitted by a uniformly accelerated mirror.Comment: 27 pages and 2 figures LaTeX2

Uniformly Accelerated Mirrors. Part 1: Mean Fluxes

The Davies-Fulling model describes the scattering of a massless field by a moving mirror in 1+1 dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blue shift effects associated with the horizons. On one hand, the Bogoliubov coefficients are ill-defined and the total energy emitted diverges. On the other hand, the instantaneous mean flux vanishes. To obtained well-defined expressions we introduce an alternative model based on an action principle. The usefulness of this model is to allow to switch on and off the interaction at asymptotically large times. By an appropriate choice of the switching function, we obtain analytical expressions for the scattering amplitudes and the fluxes emitted by the mirror. When the coupling is constant, we recover the vanishing flux. However it is now followed by transients which inevitably become singular when the switching off is performed at late time. Our analysis reveals that the scattering amplitudes (and the Bogoliubov coefficients) should be seen as distributions and not as mere functions. Moreover, our regularized amplitudes can be put in a one to one correspondence with the transition amplitudes of an accelerated detector, thereby unifying the physics of uniformly accelerated systems. In a forthcoming article, we shall use our scattering amplitudes to analyze the quantum correlations amongst emitted particles which are also ill-defined in the Davies-Fulling model in the presence of horizons.Comment: 23 pages, 7 postscript figure

Effective inhomogeneous inflation: curvature inhomogeneities of the Einstein vacuum

We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads - on average - to a spatially flat, homogeneous and isotropic universe model, providing initial conditions for pre-heating and, by the same mechanism, a possibly natural self-exit.Comment: 9 pages, 2 figures, to appear in Class. Quant. Grav. as Fast Track Communicatio

Uniformly Accelerated Mirrors. Part 2: Quantum Correlations

We study the correlations between the particles emitted by a moving mirror. To this end, we first analyze $$, the two-point function of the stress tensor of the radiation field. In this we generalize the work undertaken by Carlitz and Willey. To further analyze how the vacuum correlations on $I^-$ are scattered by the mirror and redistributed among the produced pairs of particles, we use a more powerful approach based on the value of $T_{\mu\nu}$ which is conditional to the detection of a given particle on $I^+$. We apply both methods to the fluxes emitted by a uniformly accelerated mirror. This case is particularly interesting because of its strong interferences which lead to a vanishing flux, and because of its divergences which are due to the infinite blue shift effects associated with the horizons. Using the conditional value of $T_{\mu\nu}$, we reveal the existence of correlations between created particles and their partners in a domain where the mean fluxes and the two-point function vanish. This demonstrates that the scattering by an accelerated mirror leads to a steady conversion of vacuum fluctuations into pairs of quanta. Finally, we study the scattering by two uniformly accelerated mirrors which follow symmetrical trajectories (i.e. which possess the same horizons). When using the Davies-Fulling model, the Bogoliubov coefficients encoding pair creation vanish because of perfectly destructive interferences. When using regularized amplitudes, these interferences are inevitably lost thereby giving rise to pair creation.Comment: 30 pages, 9 postscript figure

Accelerating towards P. vivax elimination with a novel serological test-and-treat strategy: a modelling case study in Brazil

BACKGROUND: Plasmodium vivax malaria is challenging to control and eliminate. Treatment with radical cure drugs fails to target the hidden asymptomatic and hypnozoite reservoirs in populations. PvSeroTAT, a novel serological test-and-treat intervention using a serological diagnostic to screen hypnozoite carriers for radical cure eligibility and treatment, could accelerate P. vivax elimination. METHODS: Using a previously developed mathematical model of P. vivax transmission adapted to the Brazilian context as a case study for implementation, we evaluate the public health impact of various deployment strategies of PvSeroTAT as a mass campaign. We compare relative reductions in prevalence, cases averted, glucose-6-phosphate dehydrogenase (G6PD) tests, and treatment doses of PvSeroTAT campaigns to strengthened case management alone or mass drug administration (MDA) campaigns across different settings. FINDINGS: Deploying a single round of PvSeroTAT with 80% coverage to treat cases with a high efficacy radical cure regimen with primaquine is predicted to reduce point population prevalence by 22.5% [95% UI: 20.2%-24.8%] in a peri-urban setting with high transmission and by 25.2% [95% UI: 9.6%-42.2%] in an occupational setting with moderate transmission. In the latter example, while a single PvSeroTAT achieves 9.2% less impact on prevalence and averts 300 less cases per 100,000 than a single MDA (25.2% [95% UI: 9.6%-42.2%] point prevalence reduction versus 34.4% [95% UI: 24.9%-44%]), PvSeroTAT requires 4.6 times less radical cure treatments and G6PD tests. Layering strengthened case management and deploying four rounds of PvSeroTAT six months apart is predicted to reduce point prevalence by a mean of 74.1% [95% UI: 61.3%-86.3%] or more in low transmission settings with less than 10 cases per 1000 population. INTERPRETATION: Modelling predicts that mass campaigns with PvSeroTAT are predicted to reduce P. vivax parasite prevalence across a range of transmission settings and require fewer resources than MDA. In combination with strengthened case management, mass campaigns of serological test-and-treat interventions can accelerate towards P. vivax elimination. FUNDING: This project was funded in part by the Bill and Melinda Gates Foundation and the National Health and Medical Research Council

Entanglement Dynamics between Inertial and Non-uniformly Accelerated Detectors

We study the time-dependence of quantum entanglement between two Unruh-DeWitt detectors, one at rest in a Minkowski frame, the other non-uniformly accelerated in some specified way. The two detectors each couple to a scalar quantum field but do not interact directly. The primary challenge in problems involving non-uniformly accelerated detectors arises from the fact that an event horizon is absent and the Unruh temperature is ill-defined. By numerical calculation we demonstrate that the correlators of the accelerated detector in the weak coupling limit behaves like those of an oscillator in a bath of time-varying "temperature" proportional to the instantaneous proper acceleration of the detector, with oscillatory modifications due to non-adiabatic effects. We find that in this setup the acceleration of the detector in effect slows down the disentanglement process in Minkowski time due to the time dilation in that moving detectorComment: 20 pages, 15 figures; References added; More analysis given in Appendix C; Typos correcte

International trade and domestic competition: Evidence from Belgium

We investigate the effect of domestic market competition on firm-level export intensity. We employ a comprehensive dataset of Belgian firms from 2005–2008, when the fall in the number of firms engaged in trade was accompanied by a growing amount of transactions. The resulting increase in the domestic concentration of Belgian firms has sparked numerous debates, since the direction of causality between domestic market structure and export performance is unclear. We apply the fractional logit estimator and control for both self-selection and simultaneity bias. We find that a positive linkage exists between the level of competition and export intensity

Unruh--DeWitt detectors in spherically symmetric dynamical space-times

In the present paper, Unruh--DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh--DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein--de Sitter universe (that is a more realistic situation in the frame of $\Lambda$CDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.Comment: 19 pages, to appear on IJTP. arXiv admin note: substantial text overlap with arXiv:1101.525