Selective Transport and Mobility Edges in Quasi-1D Systems with a Stratified Correlated Disorder

We present analytical results on transport properties of many-mode waveguides with randomly stratified disorder having long-range correlations. To describe such systems, the theory of 1D transport recently developed for a correlated disorder is generalized. The propagation of waves through such waveguides may reveal a quite unexpected phenomena of a complete transparency for a subset of propagating modes. We found that with a proper choice of long-range correlations one can arrange a perfect transparency of waveguides inside a given frequency window of incoming waves. Thus, mobility edges are shown to be possible in quasi-1D geometry with correlated disorder. The results may be important for experimental realizations of a selective transport in application to both waveguides and electron/optic nanodevices.Comment: RevTex, 4 pages, no figure

Enhanced quantum tunnelling induced by disorder

We reconsider the problem of the enhancement of tunnelling of a quantum particle induced by disorder of a one-dimensional tunnel barrier of length $L$, using two different approximate analytic solutions of the invariant imbedding equations of wave propagation for weak disorder. The two solutions are complementary for the detailed understanding of important aspects of numerical results on disorder-enhanced tunnelling obtained recently by Kim et al. (Phys. rev. B{\bf 77}, 024203 (2008)). In particular, we derive analytically the scaled wavenumber $(kL)$-threshold where disorder-enhanced tunnelling of an incident electron first occurs, as well as the rate of variation of the transmittance in the limit of vanishing disorder. Both quantities are in good agreement with the numerical results of Kim et al. Our non-perturbative solution of the invariant imbedding equations allows us to show that the disorder enhances both the mean conductance and the mean resistance of the barrier.Comment: 10 page

Fixed points of dynamic processes of set-valued F-contractions and application to functional equations

The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via the dynamic processes. The paper includes a non-trivial example which shows the motivation for such investigations. The work is summarized by the application of the introduced nonlinear F-contractions to functional equations

Influence of dynamic content on visual attention during video advertisements

Purpose Dynamic advertising, including television and online video ads, demands new theory and tools developed to understand attention to moving stimuli. The purpose of this study is to empirically test the predictions of a new dynamic attention theory, Dynamic Human-Centred Communication Systems Theory, versus the predictions of salience theory. Design/methodology/approach An eye-tracking study used a sample of consumers to measure visual attention to potential areas of interest (AOIs) in a random selection of unfamiliar video ads. An eye-tracking software feature called intelligent bounding boxes (IBBs) was used to track attention to moving AOIs. AOIs were coded for the presence of static salience variables (size, brightness, colour and clutter) and dynamic attention theory dimensions (imminence, motivational relevance, task relevance and stability). Findings Static salience variables contributed 90% of explained variance in fixation and 57% in fixation duration. However, the data further supported the three-way interaction uniquely predicted by dynamic attention theory: between imminence (central vs peripheral), relevance (motivational or task relevant vs not) and stability (fleeting vs stable). The findings of this study indicate that viewers treat dynamic stimuli like real life, paying less attention to central, relevant and stable AOIs, which are available across time and space in the environment and so do not need to be memorised. Research limitations/implications Despite the limitations of small samples of consumers and video ads, the results of this study demonstrate the potential of two relatively recent innovations, which have received limited emphasis in the marketing literature: dynamic attention theory and IBBs. Practical implications This study documents what does and does not attract attention to video advertising. What gets attention according to salience theory (e.g. central location) may not always get attention in dynamic advertising because of the effects of relevance and stability. To better understand how to execute video advertising to direct and retain attention to important AOIs, advertisers and advertising researchers are encouraged to use IBBs. Originality/value This study makes two original contributions: to marketing theory, by showing how dynamic attention theory can predict attention to video advertising better than salience theory, and to marketing research, showing the utility of tracking visual attention to moving objects in video advertising with IBBs, which appear underutilised in advertising research

Fluctuation theorem for constrained equilibrium systems

We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless finite-time averages of the phase-space contraction rate have non-trivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for non-equilibrium stationary states, and appropriate to constrained equilibrium states. Moreover we show these fluctuations are distributed according to a Gaussian curve for long-enough times. Three different systems are considered here, namely (i) a fluid composed of particles interacting with Lennard-Jones potentials; (ii) a harmonic oscillator with Nos\'e-Hoover thermostatting; (iii) a simple hyperbolic two-dimensional map.Comment: To appear in Phys. Rev.

Stiff Stability of the Hydrogen atom in dissipative Fokker electrodynamics

We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) timescale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics (QED) agree with the prediction of our resonance condition within one percent average deviation.Comment: 1 figure, Notice that Eq. (34) of the Phys. Rev. E paper has a typo; it is missing the square Brackets of eq. (33), find here the correct e

Teachers developing assessment for learning: impact on student achievement

While it is generally acknowledged that increased use of formative assessment (or assessment for learning) leads to higher quality learning, it is often claimed that the pressure in schools to improve the results achieved by students in externally-set tests and examinations precludes its use. This paper reports on the achievement of secondary school students who worked in classrooms where teachers made time to develop formative assessment strategies. A total of 24 teachers (2 science and 2 mathematics teachers, in each of six schools in two LEAs) were supported over a six-month period in exploring and planning their approach to formative assessment, and then, beginning in September 1999, the teachers put these plans into action with selected classes. In order to compute effect sizes, a measure of prior attainment and at least one comparison group was established for each class (typically either an equivalent class taught in the previous year by the same teacher, or a parallel class taught by another teacher). The mean effect size was 0.32

A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schr\"odinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.Comment: 4 page

Cosmological particle production and the precision of the WKB approximation

Particle production by slow-changing gravitational fields is usually described using quantum field theory in curved spacetime. Calculations require a definition of the vacuum state, which can be given using the adiabatic (WKB) approximation. I investigate the best attainable precision of the resulting approximate definition of the particle number. The standard WKB ansatz yields a divergent asymptotic series in the adiabatic parameter. I derive a novel formula for the optimal number of terms in that series and demonstrate that the error of the optimally truncated WKB series is exponentially small. This precision is still insufficient to describe particle production from vacuum, which is typically also exponentially small. An adequately precise approximation can be found by improving the WKB ansatz through perturbation theory. I show quantitatively that the fundamentally unavoidable imprecision in the definition of particle number in a time-dependent background is equal to the particle production expected to occur during that epoch. The results are illustrated by analytic and numerical examples.Comment: 14 pages, RevTeX, 5 figures; minor changes, a clarification in Sec. II

Exact transmission moments in one-dimensional weak localization and single-parameter scaling

We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection coefficients to fourth order in the weakly disordered site energies. These results confirm the validity of single-parameter scaling theory in a domain where the higher transmission cumulants may be neglected. We compare our results with earlier results for transmission cumulants in the weak localization domain based on the phase randomization hypothesis