482 research outputs found
Quasiperiodic tilings under magnetic field
We study the electronic properties of a two-dimensional quasiperiodic tiling,
the isometric generalized Rauzy tiling, embedded in a magnetic field. Its
energy spectrum is computed in a tight-binding approach by means of the
recursion method. Then, we study the quantum dynamics of wave packets and
discuss the influence of the magnetic field on the diffusion and spectral
exponents. Finally, we consider a quasiperiodic superconducting wire network
with the same geometry and we determine the critical temperature as a function
of the magnetic field.Comment: 6 pages, 5 EPS figure
A unified projection formalism for the Al-Pd-Mn quasicrystal Xi-approximants and their metadislocations
The approximants xi, xi' and xi'_n of the quasicrystal Al-Mn-Pd display most
interesting plastic properties as for example phason-induced deformation
processes (Klein, H., Audier, M., Boudard, M., de Boissieu, M., Beraha, L., and
Duneau, M., 1996, Phil. Mag. A, 73, 309.) or metadislocations (Klein, H.,
Feuerbacher, M., Schall, P., and Urban, K., 1999, Phys. Rev. Lett., 82, 3468.).
Here we demonstrate that the phases and their deformed or defected states can
be described by a simple projection formalism in three-dimensional space - not
as usual in four to six dimensions. With the method we can interpret
microstructures observed with electron microscopy as phasonic phase boundaries.
Furthermore we determine the metadislocations of lowest energy and relate them
uniquely to experimentally observed ones. Since moving metadislocations in the
xi'-phase can create new phason-planes, we suggest a dislocation induced phase
transition from xi' to xi'_n. The methods developed in this paper can as well
be used for various other complex metallic alloys.Comment: 25 pages, 12 figure
Flip dynamics in octagonal rhombus tiling sets
We investigate the properties of classical single flip dynamics in sets of
two-dimensional random rhombus tilings. Single flips are local moves involving
3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We
determine the ergodic times of these dynamical systems (at infinite
temperature): they grow with the system size like ;
these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets
and a powerful tool from probability theory, the coupling technique. We also
point out the interesting occurrence of Gumbel distributions.Comment: 5 Revtex pages, 4 figures; definitive versio
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