Module categories over graded fusion categories

AbstractLet C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,α) of C. We also describe functor categories over C (and in particular the dual categories of C). We use this in order to classify module categories over the Tambara Yamagami fusion categories, and their duals

Ultrasmall volume Plasmons - yet with complete retardation effects

Nano particle-plasmons are attributed to quasi-static oscillation with no wave propagation due to their subwavelength size. However, when located within a band-gap medium (even in air if the particle is small enough), the particle interfaces are acting as wave-mirrors, incurring small negative retardation. The latter when compensated by a respective (short) propagation within the particle substantiates a full-fledged resonator based on constructive interference. This unusual wave interference in the deep subwavelength regime (modal-volume<0.001lambda^3) significantly enhances the Q-factor, e.g. 50 compared to the quasi-static limit of 5.5.Comment: 16 pages, 6 figure

Generalized conductance sum rule in atomic break junctions

When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels (valence orbitals of the junction atom) undergo strong variations. We propose a microscopic explanation of this phenomenon, based on Coulomb correlation effects between electrons in valence orbitals of the junction atom. The resulting approximate conductance quantization is closely related to the Friedel sum rule.Comment: 4 pages, 1 figure, appears in Proceedings of the NATO Advanced Research Workshop ``Size dependent magnetic scattering'', Pecs, Hungary, May 28 - June 1, 200

On the Synthesis of Optimal Control Laws

In this paper we advocate for Isaacs\u27 method for the solution of differential games to be applied to the solution of optimal control problems. To make the argument, the vehicle employed is Pontryagin\u27s canonical optimal control example, which entails a double integrator plant. However, rather than controlling the state to the origin, we correctly require the end state to reach a terminal set that contains the origin in its interior. Indeed, in practice, it is required to control to a prescribed tolerance rather than reach a desired end state; achieving tight tolerances is expensive, and from a theoretical point of view, constraining the end state to a terminal manifold of co-dimension n-1 renders the optimal control problem well-posed. Thus, the correct solution of the optimal control problem is obtained. In this respect, two target sets are considered: a smooth circular target and a square target with corners; obviously, the size of the target sets can be shrunk to become very small. Closed-loop state-feedback control laws are developed which drive the double integrator plant from an arbitrary initial state to the target set in minimum time. This is accomplished using Isaacs\u27 method for the solution of differential games, which entails Dynamic Programming (DP), working backward from the Usable Part (UP) of the target set, as opposed to obtaining the optimal trajectories using the necessary conditions provided by Pontryagin\u27s Maximum Principle (PMP). Special attention is given to the critical UP of the target set in the process of obtaining the global solution of the optimal control problem at hand. In this paper, Isaacs\u27 method for the solution of differential games is applied to the solution of optimal control problems and the juxtaposition of the PMP and DP is undertaken

Enhancement of quantum dot peak-spacing fluctuations in the fractional q uantum Hall regime

The fluctuations in the spacing of the tunneling resonances through a quantum dot have been studied in the quantum Hall regime. Using the fact that the ground-state of the system is described very well by the Laughlin wavefunction, we were able to determine accurately, via classical Monte Carlo calculations, the amplitude and distribution of the peak-spacing fluctuations. Our results clearly demonstrate a big enhancement of the fluctuations as the importance of the electronic correlations increases, namely as the density decreases and filling factor becomes smaller. We also find that the distribution of the fluctuations approaches a Gaussian with increasing density of random potentials.Comment: 6 pages, 3 figures all in gzipped tarred fil

Multiple perspectives on cognitive development: Radical constructivism, cognitive constructivism, sociocultural theory, and critical theory

This multi-vocal article represents the work of three teacher educators. In conjunction with Glasersfeld’s (1996) description of Radical Constructivism, we agree that any theory “cannot claim to be anything but one approach to the age-old problem of knowing. Only its application in contexts where a theory of knowing makes a difference can show whether or not it can be considered a viable approach.” (von Glasersfeld, 1996, p. 309). In this conceptual piece, we examined the relationship between Radical Constructivism and three distinct, yet sometimes overlapping, theories: 1) Cognitive Constructivism 2) Sociocultural Theory; and 3) Critical Theory. First, we discuss the key premises, elements, and/or assumptions of each theory as well as points of convergence and divergence between each theory and Radical Constructivism. Secondly, we will analyze the opening vignette through the three different theoretical lenses

Effect of Quantum Confinement on Electron Tunneling through a Quantum Dot

Employing the Anderson impurity model, we study tunneling properties through an ideal quantum dot near the conductance minima. Considering the Coulomb blockade and the quantum confinement on an equal footing, we have obtained current contributions from various types of tunneling processes; inelastic cotunneling, elastic cotunneling, and resonant tunneling of thermally activated electrons. We have found that the inelastic cotunneling is suppressed in the quantum confinement limit, and thus the conductance near its minima is determined by the elastic cotunneling at low temperature ($k_BT \ll \Gamma$, $\Gamma$: dot-reservoir coupling constant), or by the resonant tunneling of single electrons at high temperature ($k_BT \gg \Gamma$).Comment: 11 pages Revtex, 2 Postscript figures, To appear in Phys.Rev.

Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in the presence of a magnetic field B. These effects arise from the interference between phase factors associated with different electron paths connecting two distinct sites. For electrons confined on a square lattice, with and without disorder, we obtain closed-form expressions for the tunneling probability, which determines the conductivity, between two arbitrary sites by exactly summing the corresponding phase factors of all forward-scattering paths connecting them. An analytic field-dependent expression, valid in any dimension, for the magnetoconductance (MC) is derived. A positive MC is clearly observed when turning on the magnetic field. In 2D, when the strength of B reaches a certain value, which is inversely proportional to twice the hopping length, the MC is increased by a factor of two compared to that at zero field. We also investigate transport on the much less-studied and experimentally important 3D cubic lattice case, where it is shown how the interference patterns and the small-field behavior of the MC vary according to the orientation of B. The effect on the low-flux MC due to the randomness of the angles between the hopping direction and the orientation of B is also examined analytically.Comment: 24 pages, RevTeX, 8 figures include

Reply to Comment on "Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization"

We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect \emph{a priori} to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the transfer matrix techniques for the multi-dimensional Anderson localization problem are discussed.Comment: 4 pages, accepted for publication in J.Phys.: Condens. Mat

Anomalous magnetic splitting of the Kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for nonzero magnetic field and Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulae are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large-N approaches to spin-1/2 impurities at finite magnetic field is suggested.Comment: 4 pages, 2 eps figures; published versio