7,900 research outputs found
Oversampling in shift-invariant spaces with a rational sampling period
8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y TecnologĂa
A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions
To show a mechanism leading to the breakdown of a particle picture for the
multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high
dimensions, we investigate the corresponding 2- nonlinear Schr{\"o}dinger
equation (Gross-Pitaevskii equation) with use of a modified variational
principle. A molecule of two identical Gaussian wavepackets has two degrees of
freedom(DFs), the separation of center-of-masses and the wavepacket width.
Without the inter-component interaction(ICI) these DFs show independent regular
oscillations with the degenerate eigen-frequencies. The inclusion of ICI
strongly mixes these DFs, generating a fat mode that breaks a particle picture,
which however can be recovered by introducing a time-periodic ICI with zero
average. In case of the molecule of three wavepackets for a three-component
BEC, the increase of amplitude of ICI yields a transition from regular to
chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure
Probing for Instanton Quarks with epsilon-Cooling
We use epsilon-cooling, adjusting at will the order a^2 corrections to the
lattice action, to study the parameter space of instantons in the background of
non-trivial holonomy and to determine the presence and nature of constituents
with fractional topological charge at finite and zero temperature for SU(2). As
an additional tool, zero temperature configurations were generated from those
at finite temperature with well-separated constituents. This is achieved by
"adiabatically" adjusting the anisotropic coupling used to implement finite
temperature on a symmetric lattice. The action and topological charge density,
as well as the Polyakov loop and chiral zero-modes are used to analyse these
configurations. We also show how cooling histories themselves can reveal the
presence of constituents with fractional topological charge. We comment on the
interpretation of recent fermion zero-mode studies for thermalized ensembles at
small temperatures.Comment: 26 pages, 14 figures in 33 part
Instanton classical solutions of SU(3) fixed point actions on open lattices
We construct instanton-like classical solutions of the fixed point action of
a suitable renormalization group transformation for the SU(3) lattice gauge
theory. The problem of the non-existence of one-instantons on a lattice with
periodic boundary conditions is circumvented by working on open lattices. We
consider instanton solutions for values of the size (0.6-1.9 in lattice units)
which are relevant when studying the SU(3) topology on coarse lattices using
fixed point actions. We show how these instanton configurations on open
lattices can be taken into account when determining a few-couplings
parametrization of the fixed point action.Comment: 23 pages, LaTeX, 4 eps figures, epsfig.sty; some comments adde
Structural instability of vortices in Bose-Einstein condensates
In this paper we study a gaseous Bose-Einstein condensate (BEC) and show
that: (i) A minimum value of the interaction is needed for the existence of
stable persistent currents. (ii) Vorticity is not a fundamental invariant of
the system, as there exists a conservative mechanism which can destroy a vortex
and change its sign. (iii) This mechanism is suppressed by strong interactions.Comment: 4 pages with 3 figures. Submitted to Phys. Rev. Let
Scaling law for topologically ordered systems at finite temperature
Understanding the behaviour of topologically ordered lattice systems at
finite temperature is a way of assessing their potential as fault-tolerant
quantum memories. We compute the natural extension of the topological
entanglement entropy for T > 0, namely the subleading correction
to the area law for mutual information. Its dependence on T
can be written, for Abelian Kitaev models, in terms of information-theoretic
functions and readily identifiable scaling behaviour, from which the interplay
between volume, temperature, and topological order, can be read. These
arguments are extended to non-Abelian quantum double models, and numerical
results are given for the model, showing qualitative agreement with
the Abelian case.Comment: 4 pages, 2 figure
Exact renormalization in quantum spin chains
We introduce a real-space exact renormalization group method to find exactly
solvable quantum spin chains and their ground states. This method allows us to
provide a complete list for exact solutions within SU(2) symmetric quantum spin
chains with and nearest-neighbor interactions, as well as examples
with S=5. We obtain two classes of solutions: One of them converges to the
fixed points of renormalization group and the ground states are matrix product
states. Another one does not have renormalization fixed points and the ground
states are partially ferromagnetic states.Comment: 8 pages, 5 figures, references added, published versio
Interaction Effects on the Magneto-optical Response of Magnetoplasmonic Dimers
The effect that dipole-dipole interactions have on the magneto-optical (MO)
properties of magnetoplasmonic dimers is theoretically studied. The specific
plasmonic versus magnetoplasmonic nature of the dimer's metallic components and
their specific location within the dimer plays a crucial role on the
determination of these properties. We find that it is possible to generate an
induced MO activity in a purely plasmonic component, even larger than that of
the MO one, therefore dominating the overall MO spectral dependence of the
system. Adequate stacking of these components may allow obtaining, for specific
spectral regions, larger MO activities in systems with reduced amount of MO
metal and therefore with lower optical losses. Theoretical results are
contrasted and confirmed with experiments for selected structures
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