Green's Function of 3-D Helmholtz Equation for Turbulent Medium: Application to Optics

The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is given approximately by the superposition integral, which is a mathematical expression of the extended Huygens-Fresnel principle. In doing so, it is important to find the atmospheric impulse response (Green's function). Within a limited but useful region of validity, a satisfactory optical propagation theory for the earth's clear turbulent atmosphere could be developed by using Rytov's method to approximate the Helmholtz equation. In particular, we deal with two optical problems which are the time reversal and apodization problems. The background and consequences of these results for optical communication through the atmosphere are briefly discussed

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published versio

Decoherence and entropy of primordial fluctuations II. The entropy budget

We calculate the entropy of adiabatic perturbations associated with a truncation of the hierarchy of Green functions at the first non trivial level, i.e. in a self-consistent Gaussian approximation. We give the equation governing the entropy growth and discuss its phenomenology. It is parameterized by two model-dependent kernels. We then examine two particular inflationary models, one with isocurvature perturbations, the other with corrections due to loops of matter fields. In the first model the entropy grows rapidely, while in the second the state remains pure (at one loop).Comment: 28 page

Constructing QFT's wherein Lorentz Invariance is broken by dissipative effects in the UV

There has been a recent interest in considering Quantum Field Theories in which Lorentz Invariance is broken in the UV sector. However attention has been mostly limited to dispersive theories. In this work we provide the generalized settings for studying dissipation. Unitarity is preserved by coupling the original fields to additional (heavy) fields which induce the dissipation. Starting with Lagrangians breaking LI in the UV, we learn that dissipative effects unavoidably develop in the effective theory. We then covariantize these Lagrangians in order to address the trans-Planckian question of inflation and black hole physics. The peculiar properties of the additional fields inducing dissipation is revealed by the covariantization. The links with the phenomenological approach to Quantum Gravity and with some Brane World scenarios are also discussed.Comment: 31 pages, 1 Figure, Proceedings of the SISSA conference: ``From Quantum to Emergent Gravity'' june 2007, * Added comments and reference

The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic states of low order and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all imposed at the bounce. The adiabatic spectra are typically suppressed at large scales, and display rapid oscillations with an increase of power at intermediate scales. In the non-oscillating vacuum, there is power suppression for large scales, but the rapid oscillations are absent. We argue that the oscillations are due to the imposition of initial adiabatic conditions in the region of kinetic dominance, and that they would also be present in General Relativity. Finally, we discuss the sensitivity of our results to changes of the initial time and other data of the model.Comment: 29 pages, 13 figure

Scattering theory from microscopic first principles

We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the flux-across-surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave function---even for an, inevitably inadequate, orthodox derivation.Comment: To appear in Physica A, May 200

Gravitational waves in non-singular string cosmologies

We study the evolution of tensor metric fluctuations in a class of non-singular models based on the string effective action, by including in the perturbation equation the higher-derivative and loop corrections needed to regularise the background solutions. We discuss the effects of such higher-order corrections on the final graviton spectrum, and we compare the results of analytical and numerical computations.Comment: 24 pages, 7 figure