Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions

We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square displacement versus time generated here show that the motion is a kind of anomalous diffusion with the diffusion coefficient depending on the self-similar rates. In addition, it is found that the distribution of displacement agrees to a reliable precision with the q-Gaussian type distribution in some cases and bimodal distribution in some other cases. The results obtained show that the self-similar motion may be used to describe the anomalous diffusion and nonextensive statistical distributions.Comment: 15pages, 5figure

Using tasks to explore teacher knowledge in situation-specific contexts

This article was published in the journal, Journal of Mathematics Teacher Education [© Springer] and the original publication is available at www.springerlink.comResearch often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of x+x−1=0 of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore

Supersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.Comment: 17 pages, latex, no figure

In-flight calibration of STEREO-B/WAVES antenna system

The STEREO/WAVES (SWAVES) experiment on board the two STEREO spacecraft (Solar Terrestrial Relations Observatory) launched on 25 October 2006 is dedicated to the measurement of the radio spectrum at frequencies between a few kilohertz and 16 MHz. The SWAVES antenna system consists of 6 m long orthogonal monopoles designed to measure the electric component of the radio waves. With this configuration direction finding of radio sources and polarimetry (analysis of the polarization state) of incident radio waves is possible. For the evaluation of the SWAVES data the receiving properties of the antennas, distorted by the radiation coupling with the spacecraft body and other onboard devices, have to be known accurately. In the present context, these properties are described by the antenna effective length vectors. We present the results of an in-flight calibration of the SWAVES antennas using the observations of the nonthermal terrestrial auroral kilometric radiation (AKR) during STEREO roll maneuvers in an early stage of the mission. A least squares method combined with a genetic algorithm was applied to find the effective length vectors of the STEREO Behind (STEREO-B)/WAVES antennas in a quasi-static frequency range ($L_{antenna} \ll \lambda_{wave}$) which fit best to the model and observed AKR intensity profiles. The obtained results confirm the former SWAVES antenna analysis by rheometry and numerical simulations. A final set of antenna parameters is recommended as a basis for evaluations of the SWAVES data

Many-worlds interpretation of quantum theory and mesoscopic anthropic principle

We suggest to combine the Anthropic Principle with Many-Worlds Interpretation of Quantum Theory. Realizing the multiplicity of worlds it provides an opportunity of explanation of some important events which are assumed to be extremely improbable. The Mesoscopic Anthropic Principle suggested here is aimed to explain appearance of such events which are necessary for emergence of Life and Mind. It is complementary to Cosmological Anthropic Principle explaining the fine tuning of fundamental constants. We briefly discuss various possible applications of Mesoscopic Anthropic Principle including the Solar Eclipses and assembling of complex molecules. Besides, we address the problem of Time's Arrow in the framework of Many-World Interpretation. We suggest the recipe for disentangling of quantities defined by fundamental physical laws and by an anthropic selection.Comment: 11 page

Fracton pairing mechanism for "strange" superconductors: Self-assembling organic polymers and copper-oxide compounds

Self-assembling organic polymers and copper-oxide compounds are two classes of "strange" superconductors, whose challenging behavior does not comply with the traditional picture of Bardeen, Cooper, and Schrieffer (BCS) superconductivity in regular crystals. In this paper, we propose a theoretical model that accounts for the strange superconducting properties of either class of the materials. These properties are considered as interconnected manifestations of the same phenomenon: We argue that superconductivity occurs in the both cases because the charge carriers (i.e., electrons or holes) exchange {\it fracton excitations}, quantum oscillations of fractal lattices that mimic the complex microscopic organization of the strange superconductors. For the copper oxides, the superconducting transition temperature $T_c$ as predicted by the fracton mechanism is of the order of $\sim 150$ K. We suggest that the marginal ingredient of the high-temperature superconducting phase is provided by fracton coupled holes that condensate in the conducting copper-oxygen planes owing to the intrinsic field-effect-transistor configuration of the cuprate compounds. For the gate-induced superconducting phase in the electron-doped polymers, we simultaneously find a rather modest transition temperature of $\sim (2-3)$ K owing to the limitations imposed by the electron tunneling processes on a fractal geometry. We speculate that hole-type superconductivity observes larger onset temperatures when compared to its electron-type counterpart. This promises an intriguing possibility of the high-temperature superconducting states in hole-doped complex materials. A specific prediction of the present study is universality of ac conduction for $T\gtrsim T_c$.Comment: 12 pages (including separate abstract page), no figure

Chaos assisted instanton tunneling in one dimensional perturbed periodic potential

For the system with one-dimensional spatially periodic potential we demonstrate that small periodic in time perturbation results in appearance of chaotic instanton solutions. We estimate parameter of local instability, width of stochastic layer and correlator for perturbed instanton solutions. Application of the instanton technique enables to calculate the amplitude of the tunneling, the form of the spectrum and the lower bound for width of the ground quasienergy zone

Decoherence, Chaos, and the Second Law

We investigate implications of decoherence for quantum systems which are classically chaotic. We show that, in open systems, the rate of von Neumann entropy production quickly reaches an asymptotic value which is: (i) independent of the system-environment coupling, (ii) dictated by the dynamics of the system, and (iii) dominated by the largest Lyapunov exponent. These results shed a new light on the correspondence between quantum and classical dynamics as well as on the origins of the ``arrow of time.''Comment: 13 Pages, 2 Figures available upon request, Preprint LA-UR-93-, The new version contains the text, the previous one had only the Macros: sorry

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.Comment: 15 pages, standard LaTe