Surface structure of i-Al(68)Pd(23)Mn(9): An analysis based on the T*(2F) tiling decorated by Bergman polytopes

A Fibonacci-like terrace structure along a 5fold axis of i-Al(68)Pd(23)Mn(9) monograins has been observed by T.M. Schaub et al. with scanning tunnelling microscopy (STM). In the planes of the terraces they see patterns of dark pentagonal holes. These holes are well oriented both within and among terraces. In one of 11 planes Schaub et al. obtain the autocorrelation function of the hole pattern. We interpret these experimental findings in terms of the Katz-Gratias-de Boisseu-Elser model. Following the suggestion of Elser that the Bergman clusters are the dominant motive of this model, we decorate the tiling T*(2F) by the Bergman polytopes only. The tiling T*(2F) allows us to use the powerful tools of the projection techniques. The Bergman polytopes can be easily replaced by the Mackay polytopes as the decoration objects. We derive a picture of ``geared'' layers of Bergman polytopes from the projection techniques as well as from a huge patch. Under the assumption that no surface reconstruction takes place, this picture explains the Fibonacci-sequence of the step heights as well as the related structure in the terraces qualitatively and to certain extent even quantitatively. Furthermore, this layer-picture requires that the polytopes are cut in order to allow for the observed step heights. We conclude that Bergman or Mackay clusters have to be considered as geometric building blocks of the i-AlPdMn structure rather than as energetically stable entities

Fractional charges in pyrochlore lattices

A pyrochlore lattice is considered where the average electron number of electrons per site is half--integer, concentrating on the case of exactly half an electron per site. Strong on-site repulsions are assumed, so that all sites are either empty or singly occupied. Where there are in addition strong nearest--neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge (+/-) e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge -e/2, connected by a Heisenberg spin chain which carries the electron's spin.Comment: 10 pages, 4 eps figures. To appear in Decemeber issue of Annalen der Physi

Jamming under tension in polymer crazes

Molecular dynamics simulations are used to study a unique expanded jammed state. Tension transforms many glassy polymers from a dense glass to a network of fibrils and voids called a craze. Entanglements between polymers and interchain friction jam the system after a fixed increase in volume. As in dense jammed systems, the distribution of forces is exponential, but they are tensile rather than compressive. The broad distribution of forces has important implications for fibril breakdown and the ultimate strength of crazes.Comment: 4 pages, 4 figure

Limitations on the smooth confinement of an unstretchable manifold

We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball B_r^d \subset {\mathbb R}^d of radius r < 1/2 unless one of two conditions is met -- (1)The embedding manifold has dimension d >= 2m. (2) The embedding is not smooth. The proof uses differential geometry to show that if d<2m and the embedding is smooth and isometric, we can construct a line from the center of D^m to the boundary that is geodesic in both D^m and in the embedding manifold {\mathbb R}^d. Since such a line has length 1, the diameter of the embedding ball must exceed 1.Comment: 20 Pages, 3 Figure

Revivals of quantum wave-packets in graphene

We investigate the propagation of wave-packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time-evolution of an initially localised wave-packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac-Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.Comment: 22 pages, 10 figures, 3 movies, to appear in New Journal of Physic

Interference in interacting quantum dots with spin

We study spectral and transport properties of interacting quantum dots with spin. Two particular model systems are investigated: Lateral multilevel and two parallel quantum dots. In both cases different paths through the system can give rise to interference. We demonstrate that this strengthens the multilevel Kondo effect for which a simple two-stage mechanism is proposed. In parallel dots we show under which conditions the peak of an interference-induced orbital Kondo effect can be split.Comment: 8 pages, 8 figure

Tunneling out of a time-dependent well

Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent Hamiltonians which are not higher than quadratic in the position operator, like i.e the driven harmonic oscillator with time-dependent frequency. The second class is related to the existence of additional invariants in the Hamiltonian, which can be used to map the solution of the time-dependent problem to that of a related time-independent one. In this article we discuss and develop analytic methods for solving time-dependent tunneling problems, which cannot be addressed by using quadratic Hamiltonians. Specifically, we give an analytic solution to the problem of tunneling from an attractive time-dependent potential which is embedded in a long-range repulsive potential. Recent progress in atomic physics makes it possible to observe experimentally time-dependent phenomena and record the probability distribution over a long range of time. Of special interest is the observation of macroscopical quantum-tunneling phenomena in Bose-Einstein condensates with time-dependent trapping potentials. We apply our model to such a case in the last section.Comment: 11 pages, 3 figure

Characterization of Active Main Belt Object P/2012 F5 (Gibbs): A Possible Impacted Asteroid

In this work we characterize the recently discovered active main belt object P/2012 F5 (Gibbs), which was discovered with a dust trail > 7' in length in the outer main belt, 7 months prior to aphelion. We use optical imaging obtained on UT 2012 March 27 to analyze the central condensation and the long trail. We find nuclear B-band and R-band apparent magnitudes of 20.96 and 19.93 mag, respectively, which give an upper limit on the radius of the nucleus of 2.1 km. The geometric cross-section of material in the trail was ~ 4 x 10^8 m^2, corresponding to a dust mass of ~ 5 x 10^7 kg. Analysis of infrared images taken by the Wide-Field Infrared Survey Explorer in September 2010 reveals that the object was below the detection limit, suggesting that it was less active than it was during 2012, or possibly inactive, just 6 months after it passed through perihelion. We set a 1-sigma upper limit on its radius during this time of 2.9 km. P/2012 F5 (Gibbs) is dynamically stable in the outer main belt on timescales of ~ 1 Gyr, pointing towards an asteroidal origin. We find that the morphology of the ejected dust is consistent with it being produced by a single event that occurred on UT 2011 July 7 $\pm$ 20 days, possibly as the result of a collision with a small impactor.Comment: 29 pages, 5 figures. Accepted for publication in Ap