9,393 research outputs found
Speed-of-light pulses in a nonlinear Weyl equation
We introduce a prototypical nonlinear Weyl equation, motivated by recent
developments in massless Dirac fermions, topological semimetals and photonics.
We study the dynamics of its pulse solutions and find that a localized one-hump
initial condition splits into a localized two-hump pulse, while an associated
phase structure emerges in suitable components of the spinor field. For times
larger than a transient time this pulse moves with the speed of light (or
Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics
and maintaining its shape (both in two and three dimensions). We show that for
the considered nonlinearity, this pulse represents an exact solution of the
nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the
results to a broader class of nonlinearities and on their emerging potential
for observation in different areas of application.Comment: 7 pages, 6 figure
Bright and dark breathers in Fermi-Pasta-Ulam lattices
In this paper we study the existence and linear stability of bright and dark
breathers in one-dimensional FPU lattices. On the one hand, we test the range
of validity of a recent breathers existence proof [G. James, {\em C. R. Acad.
Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations.
Approximate analytical expressions for small amplitude bright and dark
breathers are found to fit very well exact numerical solutions even far from
the top of the phonon band. On the other hand, we study numerically large
amplitude breathers non predicted in the above cited reference. In particular,
for a class of asymmetric FPU potentials we find an energy threshold for the
existence of exact discrete breathers, which is a relatively unexplored
phenomenon in one-dimensional lattices. Bright and dark breathers superposed on
a uniformly stressed static configuration are also investigated.Comment: 11 pages, 16 figure
Breathers in FPU systems, near and far from the phonon band
There exists a recent mathematical proof on the existence of small amplitude
breathers in FPU systems near the phonon band, which includes a prediction of
their amplitude and width. In this work we obtain numerically these breathers,
and calculate the range of validity of the predictions, which extends
relatively far from the phonon band. There exist also large amplitude breathers
with the same frequency, with the consequence that there is an energy gap for
breather creation in these systems.Comment: 3 pages, 2 figures, proceeding of the conference on Localization and
to and Energy Transfer in Nonlinear Systems, June 17-21, 2002, San Lorenzo de
El Escorial, Madrid, Spain. To be published by World Scientifi
Nonlinear localized modes in two-dimensional electrical lattices
We report the observation of spontaneous localization of energy in two
spatial dimensions in the context of nonlinear electrical lattices. Both
stationary and traveling self-localized modes were generated experimentally and
theoretically in a family of two-dimensional square, as well as hon- eycomb
lattices composed of 6x6 elements. Specifically, we find regions in driver
voltage and frequency where stationary discrete breathers, also known as
intrinsic localized modes (ILM), exist and are stable due to the interplay of
damping and spatially homogeneous driving. By introduc- ing additional
capacitors into the unit cell, these lattices can controllably induce traveling
discrete breathers. When more than one such ILMs are experimentally generated
in the lattice, the interplay of nonlinearity, discreteness and wave
interactions generate a complex dynamics wherein the ILMs attempt to maintain a
minimum distance between one another. Numerical simulations show good agreement
with experimental results, and confirm that these phenomena qualitatively carry
over to larger lattice sizes.Comment: 5 pages, 6 figure
Stability of non-time-reversible phonobreathers
Non-time reversible phonobreathers are non-linear waves that can transport
energy in coupled oscillator chains by means of a phase-torsion mechanism. In
this paper, the stability properties of these structures have been considered.
It has been performed an analytical study for low-coupling solutions based upon
the so called {\em multibreather stability theorem} previously developed by
some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms
the analytical predictions and gives a detailed picture of the existence and
stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010
Lower and upper estimates on the excitation threshold for breathers in DNLS lattices
We propose analytical lower and upper estimates on the excitation threshold
for breathers (in the form of spatially localized and time periodic solutions)
in DNLS lattices with power nonlinearity. The estimation depending explicitly
on the lattice parameters, is derived by a combination of a comparison argument
on appropriate lower bounds depending on the frequency of each solution with a
simple and justified heuristic argument. The numerical studies verify that the
analytical estimates can be of particular usefulness, as a simple analytical
detection of the activation energy for breathers in DNLS lattices.Comment: 10 pages, 3 figure
Multibreather and vortex breather stability in Klein--Gordon lattices: Equivalence between two different approaches
In this work, we revisit the question of stability of multibreather
configurations, i.e., discrete breathers with multiple excited sites at the
anti-continuum limit of uncoupled oscillators. We present two methods that
yield quantitative predictions about the Floquet multipliers of the linear
stability analysis around such exponentially localized in space, time-periodic
orbits, based on the Aubry band method and the MacKay effective Hamiltonian
method and prove that their conclusions are equivalent. Subsequently, we
showcase the usefulness of the methods by a series of case examples including
one-dimensional multi-breathers, and two-dimensional vortex breathers in the
case of a lattice of linearly coupled oscillators with the Morse potential and
in that of the discrete model
Testing equivalence of pure quantum states and graph states under SLOCC
A set of necessary and sufficient conditions are derived for the equivalence
of an arbitrary pure state and a graph state on n qubits under stochastic local
operations and classical communication (SLOCC), using the stabilizer formalism.
Because all stabilizer states are equivalent to a graph state by local unitary
transformations, these conditions constitute a classical algorithm for the
determination of SLOCC-equivalence of pure states and stabilizer states. This
algorithm provides a distinct advantage over the direct solution of the
SLOCC-equivalence condition for an unknown invertible local operator S, as it
usually allows for easy detection of states that are not SLOCC-equivalent to
graph states.Comment: 9 pages, to appear in International Journal of Quantum Information;
Minor typos corrected, updated references
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