Inflation, Renormalization, and CMB Anisotropies

In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio "r" to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio r= 0.12 +/- 0.06, which is forbidden by the standard prediction (r=-8n_t). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.Comment: 4 pages, jpconf.cls, to appear in the Proceedings of Spanish Relativity Meeting 2009 (ERE 09), Bilbao (Spain

Statistical characterization of phenolic-novolak structures

Three statistical methods of general validity are valuable for characterizing any polymer which results from chain polymerization of multifunctional branching monomers linked through bifunctional monomers

Spatial curvature effects on molecular transport by diffusion

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the known solution of Fick's law of diffusion in the flat space limit. In the biological context, this result would be useful in understanding the variations in the diffusion rates of integral proteins and other molecules on membranes.Comment: 10 page

Acceleration radiation, transition probabilities, and trans-Planckian physics

An important question in the derivation of the acceleration radiation, which also arises in Hawking's derivation of black hole radiance, is the need to invoke trans-Planckian physics for the quantum field that originates the created quanta. We point out that this issue can be further clarified by reconsidering the analysis in terms of particle detectors, transition probabilities, and local two-point functions. By writing down separate expressions for the spontaneous- and induced-transition probabilities of a uniformly accelerated detector, we show that the bulk of the effect comes from the natural (non trans-Planckian) scale of the problem, which largely diminishes the importance of the trans-Planckian sector. This is so, at least, when trans-Planckian physics is defined in a Lorentz invariant way. This analysis also suggests how to define and estimate the role of trans-Planckian physics in the Hawking effect itself.Comment: 19 page

Direct versus Delayed pathways in Strong-Field Non-Sequential Double Ionization

We report full-dimensionality quantum and classical calculations for double ionization of laser-driven helium at 390 nm. Good qualitative agreement is observed. We show that the classical double ionization trajectories can be divided into two distinct pathways: direct and delayed. The direct pathway, with an almost simultaneous ejection of both electrons, emerges from small laser intensities. With increasing intensity its relative importance, compared to the delayed ionization pathway, increases until it becomes the predominant pathway for total electron escape energy below around 5.25 $U_{p}$. However the delayed pathway is the predominant one for double ionization above a certain cut-off energy at all laser intensities

Relation Between Einstein And Quantum Field Equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.Comment: Latex, 24 pages. Minor changes in text from original versio

Learning Style Diversity in Post –Secondary Distance Education

During the fall semester of 2005, 153 university graduate students’ preferred learning styles were measured with the Kolb Learning Style Inventory, online version 3.1. The primary findings of the study indicated all of the learning styles and processes described by Kolb were represented in the distance learning population and suggested distance and residential learners uniquely engage the learning process. Biblical references were discussed with respect to the uniqueness displayed by study participants

Thomas-Fermi versus one- and two-dimensional regimes of a trapped dipolar Bose-Einstein condensate

We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar, pancake and spherical geometries. This also naturally gives the criteria for the mean-field one- and two-dimensional regimes. Our predictions, including the Thomas-Fermi density profiles, are shown to be in excellent agreement with numerical solutions. Importantly, the anisotropy of the interactions has a profound effect on the Thomas-Fermi/low-dimensional criteria.Comment: 5 pages, 2 figure

Acceleration of the universe, vacuum metamorphosis, and the large-time asymptotic form of the heat kernel

We investigate the possibility that the late acceleration observed in the rate of expansion of the universe is due to vacuum quantum effects arising in curved spacetime. The theoretical basis of the vacuum cold dark matter (VCDM), or vacuum metamorphosis, cosmological model of Parker and Raval is revisited and improved. We show, by means of a manifestly nonperturbative approach, how the infrared behavior of the propagator (related to the large-time asymptotic form of the heat kernel) of a free scalar field in curved spacetime causes the vacuum expectation value of its energy-momentum tensor to exhibit a resonance effect when the scalar curvature R of the spacetime reaches a particular value related to the mass of the field. we show that the back reaction caused by this resonance drives the universe through a transition to an accelerating expansion phase, very much in the same way as originally proposed by Parker and Raval. Our analysis includes higher derivatives that were neglected in the earlier analysis, and takes into account the possible runaway solutions that can follow from these higher-derivative terms. We find that the runaway solutions do not occur if the universe was described by the usual classical FRW solution prior to the growth of vacuum energy-density and negative pressure (i.e., vacuum metamorphosis) that causes the transition to an accelerating expansion of the universe in this theory.Comment: 33 pages, 3 figures. Submitted to Physical Review D15 (Dec 23, 2003). v2: 1 reference added. No other change

Quantum incompressibility of a falling Rydberg atom, and a gravitationally-induced charge separation effect in superconducting systems

Freely falling point-like objects converge towards the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum object such as a hydrogen atom prepared in a high principal-quantum-number stretch state, i.e., a circular Rydberg atom, is predicted to fall more slowly that a classical point-like object, when both objects are dropped from the same height from above the Earth. This indicates that, apart from "quantum jumps," the atom exhibits a kind of "quantum incompressibility" during free fall in inhomogeneous, tidal gravitational fields like those of the Earth. A superconducting ring-like system with a persistent current circulating around it behaves like the circular Rydberg atom during free fall. Like the electronic wavefunction of the freely falling atom, the Cooper-pair wavefunction is "quantum incompressible." The ions of the ionic lattice of the superconductor, however, are not "quantum incompressible," since they do not possess a globally coherent quantum phase. The resulting difference during free fall in the response of the nonlocalizable Cooper pairs of electrons and the localizable ions to inhomogeneous gravitational fields is predicted to lead to a charge separation effect, which in turn leads to a large repulsive Coulomb force that opposes the convergence caused by the tidal, attractive gravitational force on the superconducting system. A "Cavendish-like" experiment is proposed for observing the charge separation effect induced by inhomogeneous gravitational fields in a superconducting circuit. This experiment would demonstrate the existence of a novel coupling between gravity and electricity via macroscopically coherent quantum matter.Comment: `2nd Vienna Symposium for the Foundations of Modern Physics' Festschrift MS for Foundations of Physic