The Quantum Mechanics of Hyperion

This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.Comment: 17 pages, 24 figure

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

Simple bimolecular reactions $A_1+A_2\rightleftharpoons A_3+A_4$ are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction $H_2+Cl\rightleftharpoons HCl+H$, and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.Comment: 11 pages, 5 figures, to appear in vol.42 of the Brazilian Journal of Physic

Collisional cross sections and momentum distributions in astrophysical plasmas: dynamics and statistical mechanics link

We show that, in stellar core plasmas, the one-body momentum distribution function is strongly dependent, at least in the high velocity regime, on the microscopic dynamics of ion elastic collisions and therefore on the effective collisional cross sections, if a random force field is present. We take into account two cross sections describing ion-dipole and ion-ion screened interactions. Furthermore we introduce a third unusual cross section, to link statistical distributions and a quantum effect originated by the energy-momentum uncertainty owing to many-body collisions, and propose a possible physical interpretation in terms of a tidal-like force. We show that each collisional cross section gives rise to a slight peculiar correction on the Maxwellian momentum distribution function in a well defined velocity interval. We also find a possible link between microscopical dynamics of ions and statistical mechanics interpreting our results in the framework of non-extensive statistical mechanics.Comment: 8 page

Monte Carlo Exploration of Warped Higgsless Models

We have performed a detailed Monte Carlo exploration of the parameter space for a warped Higgsless model of electroweak symmetry breaking in 5 dimensions. This model is based on the $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ gauge group in an AdS$_5$ bulk with arbitrary gauge kinetic terms on both the Planck and TeV branes. Constraints arising from precision electroweak measurements and collider data are found to be relatively easy to satisfy. We show, however, that the additional requirement of perturbative unitarity up to the cut-off, $\simeq 10$ TeV, in $W_L^+W_L^-$ elastic scattering in the absence of dangerous tachyons eliminates all models. If successful models of this class exist, they must be highly fine-tuned.Comment: 26 pages, 7 figures; new fig and additional text adde

Evaluating transport in irregular pore networks

A general approach for investigating transport phenomena in porous media is presented. This approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort. The overall method combines a generalized effective medium approximation (EMA) with a macroscopic continuum model in order to derive a transport equation with explicit analytical expressions for the transport coefficients. The proposed form of the EMA is an anisotropic and heterogeneous extension of Kirkpatrick's EMA which allows the overall model to account for microscopic alterations in connectivity (with the locations of the pores and the orientation and length of the throat) as well as macroscopic variations in transport properties. A comparison to numerical results for randomly generated networks with different properties is given, indicating the potential for this methodology to handle cases that would pose significant difficulties to many other analytical models

Random paths and current fluctuations in nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems

Noncommutative Inspired Black Holes in Extra Dimensions

In a recent string theory motivated paper, Nicolini, Smailagic and Spallucci (NSS) presented an interesting model for a noncommutative inspired, Schwarzschild-like black hole solution in 4-dimensions. The essential effect of having noncommutative co-ordinates in this approach is to smear out matter distributions on a scale associated with the turn-on of noncommutativity which was taken to be near the 4-d Planck mass. In particular, NSS took this smearing to be essentially Gaussian. This energy scale is sufficiently large that in 4-d such effects may remain invisible indefinitely. Extra dimensional models which attempt to address the gauge hierarchy problem, however, allow for the possibility that the effective fundamental scale may not be far from $\sim$ 1 TeV, an energy regime that will soon be probed by experiments at both the LHC and ILC. In this paper we generalize the NSS model to the case where flat, toroidally compactified extra dimensions are accessible at the Terascale and examine the resulting modifications in black hole properties due to the existence of noncommutativity. We show that while many of the noncommutativity-induced black hole features found in 4-d by NSS persist, in some cases there can be significant modifications due the presence of extra dimensions. We also demonstrate that the essential features of this approach are not particularly sensitive to the Gaussian nature of the smearing employed by NSS.Comment: 30 pages, 12 figures; slight text modifications and references adde

Determination of Omega_b From Big Bang Nucleosynthesis in the Presence of Regions of Antimatter

Production of regions of antimatter in the early universe is predicted in many baryogenesis models. Small scale antimatter regions would annihilate during or soon after nucleosynthesis, affecting the abundances of the light elements. In this paper we study how the acceptable range in Omega_b changes in the presence of antimatter regions, as compared to the standard big bang nucleosynthesis. It turns out that it is possible to produce at the same time both a low 4He value (Y_p < 0.240) and a low D/H value (D/H < 4e-5), but overproduction of 7Li is unavoidable at large Omega_b.Comment: 9 pages, PRD version, ref. 6 correcte

Kinetic Theory of a Dilute Gas System under Steady Heat Conduction

The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.Comment: 36 pages, 4 figures, 5 table

On modified simple reacting spheres kinetic model for chemically reactive gases

Versão dos autores para esta publicação.We consider the modiffed simple reacting spheres (MSRS) kinetic model that, in addition to the conservation of energy and momentum, also preserves the angular momentum in the collisional processes. In contrast to the line-of-center models or chemical reactive models considered in [1], in the MSRS (SRS) kinetic models, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justi ed. In the MSRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard spheres-like. We consider a four component mixture A, B, A*, B*, in which the chemical reactions are of the type A + B = A* + B*, with A* and B* being distinct species from A and B. We provide fundamental physical and mathematical properties of the MSRS model, concerning the consistency of the model, the entropy inequality for the reactive system, the characterization of the equilibrium solutions, the macroscopic setting of the model and the spatially homogeneous evolution. Moreover, we show that the MSRS kinetic model reduces to the previously considered SRS model (e.g., [2], [3]) if the reduced masses of the reacting pairs are the same before and after collisions, and state in the Appendix the more important properties of the SRS system.Fundação para a Ciência e a Tecnologi