210 research outputs found
Geometrical approach to SU(2) navigation with Fibonacci anyons
Topological quantum computation with Fibonacci anyons relies on the
possibility of efficiently generating unitary transformations upon
pseudoparticles braiding. The crucial fact that such set of braids has a dense
image in the unitary operations space is well known; in addition, the
Solovay-Kitaev algorithm allows to approach a given unitary operation to any
desired accuracy. In this paper, the latter task is fulfilled with an
alternative method, in the SU(2) case, based on a generalization of the
geodesic dome construction to higher dimension.Comment: 12 pages, 5 figure
Morphological instabilities of a thin film on a Penrose lattice: a Monte Carlo study
We computed by a Monte Carlo method the thermal relaxation of a
polycrystalline thin film deposited on a Penrose lattice. The thin film was
modelled by a 2 dimensional array of elementary domains, which have each a
given height. During the Monte Carlo process, the height of each of these
elementary domains is allowed to change as well as their crystallographic
orientation. After equilibrium is reached at a given numerical temperature, all
elementary domains have changed their orientation into the same one and small
islands appear, preferentially on the domains of the Penrose lattice located in
the center of heptagons. This method is a new numerical approach to study the
influence of the substrate and its defects on the islanding process of
polycrystalline films.Comment: 9 pages,5 figure
Geometry of entangled states, Bloch spheres and Hopf fibrations
We discuss a generalization to 2 qubits of the standard Bloch sphere
representation for a single qubit, in the framework of Hopf fibrations of high
dimensional spheres by lower dimensional spheres. The single qubit Hilbert
space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented
S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres
represent the qubit overall phase degree of freedom. For the two qubits case,
the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf
fibration, with S3 fibres and a S4 base. A main striking result is that
suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation
with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.
Ab initio computation of d-d excitation energies in low-dimensional Ti and V oxychlorides
Using a quantum chemical cluster-in-solid computational scheme, we calculate
the local d-d excitation energies for two strongly correlated Mott insulators,
the oxychlorides TiOCl and VOCl. TiOCl harbors quasi-one-dimensional spin
chains made out of S = 1/2 Ti3+ ions while the electronic structure of VOCl
displays a more two-dimensional character. We find in both cases that the
lowest-energy d-d excitations are within the t2g subshell, starting at 0.34 eV
and indicating that orbital degeneracies are significantly lifted. In the
vanadium oxychloride, spin triplet to singlet excitations are calculated to be
1 eV higher in energy. For TiOCl, the computed d-level electronic structure and
the symmetries of the wavefunctions are in very good agreement with resonant
inelastic x-ray scattering results and optical absorption data. For VOCl,
future resonant inelastic x-ray scattering experiments will constitute a direct
test of the symmetry and energy of about a dozen of different d-d excitations
that we predict here
Crystallization in a model glass: influence of the boundary conditions
Using molecular dynamics calculations and the Voronoi tessellation, we study
the evolution of the local structure of a soft-sphere glass versus temperature
starting from the liquid phase at different quenching rates. This study is done
for different sizes and for two different boundary conditions namely the usual
cubic periodic boundary conditions and the isotropic hyperspherical boundary
conditions for which the particles evolve on the surface of a hypersphere in
four dimensions. Our results show that for small system sizes, crystallization
can indeed be induced by the cubic boundary conditions. On the other hand we
show that finite size effects are more pronounced on the hypersphere and that
crystallization is artificially inhibited even for large system sizes.Comment: 11 pages, 2 figure
Close Packing of Atoms, Geometric Frustration and the Formation of Heterogeneous States in Crystals
To describe structural peculiarities in inhomogeneous media caused by the
tendency to the close packing of atoms a formalism based on the using of the
Riemann geometry methods (which were successfully applied lately to the
description of structures of quasicrystals and glasses) is developed. Basing on
this formalism we find in particular the criterion of stability of precipitates
of the Frank-Kasper phases in metallic systems. The nature of the ''rhenium
effect'' in W-Re alloys is discussed.Comment: 14 pages, RevTex, 2 PostScript figure
Hard sphere crystallization gets rarer with increasing dimension
We recently found that crystallization of monodisperse hard spheres from the
bulk fluid faces a much higher free energy barrier in four than in three
dimensions at equivalent supersaturation, due to the increased geometrical
frustration between the simplex-based fluid order and the crystal [J.A. van
Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here,
we analyze the microscopic contributions to the fluid-crystal interfacial free
energy to understand how the barrier to crystallization changes with dimension.
We find the barrier to grow with dimension and we identify the role of
polydispersity in preventing crystal formation. The increased fluid stability
allows us to study the jamming behavior in four, five, and six dimensions and
compare our observations with two recent theories [C. Song, P. Wang, and H. A.
Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in
press (2009)].Comment: 15 pages, 5 figure
Geometrical Frustration: A Study of 4d Hard Spheres
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the
icosahedron and the tetrahedron is the smallest volume that can show up in
Delaunay tessalation. No periodic lattice is consistent with either and hence
these dense packings are geometrically frustrated. Because icosahedra can be
assembled from almost perfect tetrahedra, the terms "icosahedral" and
"polytetrahedral" packing are often used interchangeably, which leaves the true
origin of geometric frustration unclear. Here we report a computational study
of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible
with the symmetry of the densest crystal, while polytetrahedral order is not.
We observe that, under otherwise comparable conditions, crystal nucleation in
4d is less facile than in 3d. This suggest that it is the geometrical
frustration of polytetrahedral structures that inhibits crystallization.Comment: 4 pages, 3 figures; revised interpretatio
Gauge theory of disclinations on fluctuating elastic surfaces
A variant of a gauge theory is formulated to describe disclinations on
Riemannian surfaces that may change both the Gaussian (intrinsic) and mean
(extrinsic) curvatures, which implies that both internal strains and a location
of the surface in R^3 may vary. Besides, originally distributed disclinations
are taken into account. For the flat surface, an extended variant of the
Edelen-Kadic gauge theory is obtained. Within the linear scheme our model
recovers the von Karman equations for membranes, with a disclination-induced
source being generated by gauge fields. For a single disclination on an
arbitrary elastic surface a covariant generalization of the von Karman
equations is derived.Comment: 13 page
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