125 research outputs found
Penrose Quantum Antiferromagnet
The Penrose tiling is a perfectly ordered two dimensional structure with
fivefold symmetry and scale invariance under site decimation. Quantum spin
models on such a system can be expected to differ significantly from more
conventional structures as a result of its special symmetries. In one
dimension, for example, aperiodicity can result in distinctive quantum
entanglement properties. In this work, we study ground state properties of the
spin-1/2 Heisenberg antiferromagnet on the Penrose tiling, a model that could
also be pertinent for certain three dimensional antiferromagnetic
quasicrystals. We show, using spin wave theory and quantum Monte Carlo
simulation, that the local staggered magnetizations strongly depend on the
local coordination number z and are minimized on some sites of five-fold
symmetry. We present a simple explanation for this behavior in terms of
Heisenberg stars. Finally we show how best to represent this complex
inhomogeneous ground state, using the "perpendicular space" representation of
the tiling.Comment: 4 pages, 5 figure
Icosahedral multi-component model sets
A quasiperiodic packing Q of interpenetrating copies of C, most of them only
partially occupied, can be defined in terms of the strip projection method for
any icosahedral cluster C. We show that in the case when the coordinates of the
vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the
superspace can be reduced, namely, Q can be re-defined as a multi-component
model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl
Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals
The quasi-unit cell picture describes the atomic structure of quasicrystals
in terms of a single, repeating cluster which overlaps neighbors according to
specific overlap rules. In this paper, we discuss the precise relationship
between a general atomic decoration in the quasi-unit cell picture atomic
decorations in the Penrose tiling and in related tiling pictures. Using these
relations, we obtain a simple, practical method for determining the density,
stoichiometry and symmetry of a quasicrystal based on the atomic decoration of
the quasi-unit cell taking proper account of the sharing of atoms between
clusters.Comment: 14 pages, 8 figure
Generalized quasiperiodic Rauzy tilings
We present a geometrical description of new canonical -dimensional
codimension one quasiperiodic tilings based on generalized Fibonacci sequences.
These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual
Penrose and icosahedral tilings. Thanks to a natural indexing of the sites
according to their local environment, we easily write down, for any
approximant, the sites coordinates, the connectivity matrix and we compute the
structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change
Spin waves and local magnetizations on the Penrose tiling
We consider a Heisenberg antiferromagnet on the Penrose tiling, a
quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin
wave energies and wavefunctions are studied in the linear spin wave
approximation. A linear dispersion law is found at low energies, as in other
bipartite antiferromagnets, with an effective spin wave velocity lower than in
the square lattice. Spatial properties of eigenmodes are characterized in
several different ways. At low energies, eigenstates are relatively extended,
and show multifractal scaling. At higher energies, states are more localized,
and, depending on the energy, confined to sites of a specified coordination
number. The ground state energy of this antiferromagnet, and local staggered
magnetizations are calculated. Perpendicular space projections are presented in
order to show the underlying simplicity of this "complex" ground state. A
simple analytical model, the two-tier Heisenberg star, is presented to explain
the staggered magnetization distribution in this antiferromagnetic system.Comment: 14 pages, 21 figure
Overlapping Unit Cells in 3d Quasicrystal Structure
A 3-dimensional quasiperiodic lattice, with overlapping unit cells and
periodic in one direction, is constructed using grid and projection methods
pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are
the vertices of a convex polytope P, and 4 are interior points also shared with
other neighboring unit cells. Using Kronecker's theorem the frequencies of all
possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final
versio
Shape-Dependent Thermodynamics and Non-Local Hydrodynamics in a Non-Gibbsian Steady-State of a Drift-Diffusion System
Shape-dependent thermodynamics and non-local hydrodynamics are argued to
occur in dissipative steady states of driven diffusive systems. These
predictions are confirmed by numerical simulations. Unlike power-law
correlations, these phenomena cannot be explained by a hypothesis of
``criticality''. Instead, they require the effective Hamiltonian of the system
to contain very long-range potentials, making the invariant probability
measures formally ``non-Gibbsian''.Comment: 4 pages, Latex Version 2.09, 1 Postscript figur
Classification of one-dimensional quasilattices into mutual local-derivability classes
One-dimensional quasilattices are classified into mutual local-derivability
(MLD) classes on the basis of geometrical and number-theoretical
considerations. Most quasilattices are ternary, and there exist an infinite
number of MLD classes. Every MLD class has a finite number of quasilattices
with inflation symmetries. We can choose one of them as the representative of
the MLD class, and other members are given as decorations of the
representative. Several MLD classes of particular importance are listed. The
symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS
The GANIL control system as seen from the control room
http://accelconf.web.cern.ch/AccelConf/c81/papers/fp-08.pdfInternational audienc
Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems
We study energy spectra, eigenstates and quantum diffusion for one- and
two-dimensional quasiperiodic tight-binding models. As our one-dimensional
model system we choose the silver mean or `octonacci' chain. The
two-dimensional labyrinth tiling, which is related to the octagonal tiling, is
derived from a product of two octonacci chains. This makes it possible to treat
rather large systems numerically. For the octonacci chain, one finds singular
continuous energy spectra and critical eigenstates which is the typical
behaviour for one-dimensional Schr"odinger operators based on substitution
sequences. The energy spectra for the labyrinth tiling can, depending on the
strength of the quasiperiodic modulation, be either band-like or fractal-like.
However, the eigenstates are multifractal. The temporal spreading of a
wavepacket is described in terms of the autocorrelation function C(t) and the
mean square displacement d(t). In all cases, we observe power laws for C(t) and
d(t) with exponents -delta and beta, respectively. For the octonacci chain,
0<delta<1, whereas for the labyrinth tiling a crossover is observed from
delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the
multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both
systems. Moreover, we find that the behaviour of C(t) and d(t) is independent
of the shape and the location of the initial wavepacket. We use our results to
check several relations between the diffusion exponent beta and the fractal
dimensions of energy spectra and eigenstates that were proposed in the
literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new
results adde
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