Instanton approach to the Langevin motion of a particle in a random potential

We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution function for the time a particle needs to propagate along the system (the delay time). The proposed method allows us to find the tail of the delay time distribution function and delay time moments, providing thus an exact description of the long-time dynamics. We analyze arbitrary environments covering different types of glassy dynamics: dynamics in a short-range random field, creep, and Sinai's motion.Comment: 4 pages, 1 figur

Assessing students’ engagement: A review of instruments with psychometric Qualities

Este E-Book reúne um conjunto de investigações apresentadas no “I Congresso Internacional Envolvimento dos Alunos na Escola: Perspetivas da Psicologia e Educação” (ICIEAE), organizado no âmbito do “Projeto PTDC/CPE-CED/114362/2009 - Envolvimento dos Alunos na Escola: Diferenciação e Promoção” (EAE-DP), financiado pela Fundação para a Ciência e a Tecnologia (FCT).Framework: Students Engagement in School (SES) has been occupying a central position in the discussions regarding factors of academic success and school dropout. A considerable amount of literature on this concept exists. Although its conceptualization varies according to authors and the theoretical framework they have adopted, there is a wide agreement concerning its multidimensional nature. Key dimensions of students engagement in school (i.e., cognitive, affective, behavioral and, more recently, agentic) have been described and empirically validated. Purpose:This study aimed to review the literature on assessment of students engagement in school through a focus on the psychometric characteristics of several instruments. Methodology: The present paper focuses on self-report measures which are multidimensional. These instruments were validated on heterogeneous samples. Results: Twelve self-report measures designed to measure the students engagement in school were referred, along with four other instruments targeting teachers’ perspective as well as observational measures. Conclusions: Various measures stem from different theoretical perspectives and were developed with different types of samples. Conceptual variations often expressed in the number of dimensions considered and in items content variability suggest limitations when comparing psychometric indings of different studies. Suggestions: Studies on instruments we reviewed in the present paper suggest the need for further research on the multidimensionality of school engagement construct. Research should go beyond investigation of differential and predictive validity of measures. Thus, there is little evidence regarding the validity of engagement in school measures, when investigation of effects of specific intervention programs is aimed or validity of their use in quasiexperimental studies with useful applications in the field of education

The WKB Approximation without Divergences

In this paper, the WKB approximation to the scattering problem is developed without the divergences which usually appear at the classical turning points. A detailed procedure of complexification is shown to generate results identical to the usual WKB prescription but without the cumbersome connection formulas.Comment: 13 pages, TeX file, to appear in Int. J. Theor. Phy

Space Symmetries and Quantum Behavior of Finite Energy Configurations in SU(2)-Gauge Theory

The quantum properties of localized finite energy solutions to classical Euler-Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant $g$ is constructed, taking into account the conservation laws of momentum and angular momentum (invariance of the action with respect to the group of motion M(3) of 3-dimensional Euclidean space) rigorously in every order of perturbation theory.Comment: LaTex, 17 pages typos correcte

The X-ray Emissions from the M87 Jet: Diagnostics and Physical Interpretation

We reanalyze the deep Chandra observations of the M87 jet, first examined by Wilson & Yang (2002). By employing an analysis chain that includes image deconvolution, knots HST-1 and I are fully separated from adjacent emission. We find slight but significant variations in the spectral shape, with values of $\alpha_x$ ranging from $\sim 1.2-1.6$. We use VLA radio observations, as well as HST imaging and polarimetry data, to examine the jet's broad-band spectrum and inquire as to the nature of particle acceleration in the jet. As shown in previous papers, a simple continuous injection model for synchrotron-emitting knots, in which both the filling factor, $f_{acc}$, of regions within which particles are accelerated and the energy spectrum of the injected particles are constant, cannot account for the X-ray flux or spectrum. Instead, we propose that $f_{acc}$ is a function of position and energy and find that in the inner jet, $f_{acc} \propto E_\gamma^{-0.4 \pm 0.2} \propto E_e^{-0.2 \pm 0.1}$, and in knots A and B, $f_{acc} \propto E_\gamma^{-0.7 \pm 0.2} \propto E_e^{-0.35 \pm 0.1}$, where $E_\gamma$ is the emitted photon energy and and $E_e$ is the emitting electron energy. In this model, the index $p$ of the injected electron energy spectrum ($n(E_{e}) \propto E_{e}^{-p}$) is $p=2.2$ at all locations in the jet, as predicted by models of cosmic ray acceleration by ultrarelativistic shocks. There is a strong correlation between the peaks of X-ray emission and minima of optical percentage polarization, i.e., regions where the jet magnetic field is not ordered. We suggest that the X-ray peaks coincide with shock waves which accelerate the X-ray emitting electrons and cause changes in the direction of the magnetic field; the polarization is thus small because of beam averaging.Comment: Accepted for publication in ApJ; 21 pages, 9 figures, 2 tables; abstract shortened for astro-ph; Figures 1, 7 and 8 at reduced resolutio

Inelastic Processes in the Collision of Relativistic Highly Charged Ions with Atoms

A general expression for the cross sections of inelastic collisions of fast (including relativistic) multicharged ions with atoms which is based on the genelazition of the eikonal approximation is derived. This expression is applicable for wide range of collision energy and has the standard nonrelativistic limit and in the ultrarelativistic limit coincides with the Baltz's exact solution ~\cite{art13} of the Dirac equation. As an application of the obtained result the following processes are calculated: the excitation and ionization cross sections of hydrogenlike atom; the single and double excitation and ionization of heliumlike atom; the multiply ionization of neon and argon atoms; the probability and cross section of K-vacancy production in the relativistic $U^{92+} - U^{91+}$ collision. The simple analytic formulae for the cross sections of inelastic collisions and the recurrence relations between the ionization cross sections of different multiplicities are also obtained. Comparison of our results with the experimental data and the results of other calculations are given.Comment: 25 pages, latex, 7 figures avialable upon request,submitted to PR

Semiclassical treatment of logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are considered.Comment: 6 pages, LATEX 2.09 using IOP style

Noise storm continua: power estimates for electron acceleration

We use a generic stochastic acceleration formalism to examine the power $L_{\rm in}$ (${\rm erg s^{-1}}$) input to nonthermal electrons that cause noise storm continuum emission. The analytical approach includes the derivation of the Green's function for a general second-order Fermi process, and its application to obtain the particular solution for the nonthermal electron distribution resulting from the acceleration of a Maxwellian source in the corona. We compare $L_{\rm in}$ with the power $L_{\rm out}$ observed in noise storm radiation. Using typical values for the various parameters, we find that $L_{\rm in} \sim 10^{23-26}$ ${\rm erg s^{-1}}$, yielding an efficiency estimate $\eta \equiv L_{\rm out}/L_{\rm in}$ in the range 10^{-10} \lsim \eta \lsim 10^{-6} for this nonthermal acceleration/radiation process. These results reflect the efficiency of the overall process, starting from electron acceleration and culminating in the observed noise storm emission.Comment: Accepted for publication in Solar Physic

Cosmological Production of Vector Bosons and Cosmic Microwave Background Radiation

The intensive cosmological creation of vector W, Z- bosons in the cosmological model with the relative units is considered. Field theoretical models are studied, which predict that the CMB radiation and the baryon matter in the universe can be products of decay and annihilation processes of these primordial bosons.Comment: 31 pages, 1 figur

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st