24 research outputs found
Stability of Discrete Solitons in the Presence of Parametric Driving
In this brief report, we consider parametrically driven bright solitons in
the vicinity of the anti-continuum limit. We illustrate the mechanism through
which these solitons become unstable due to the collision of the phase mode
with the continuous spectrum, or eigenvelues bifurcating thereof. We show how
this mechanism typically leads to complete destruction of the bright solitary
wave.Comment: 4 pages, 4 figure
Discrete Solitons and Vortices in Anisotropic Hexagonal and Honeycomb Lattices
In the present work, we consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. We quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation of these instabilities to be the spontaneous rearrangement of the solution, for larger values of the coupling, into localized waveforms typically centered over fewer sites than the original unstable structure. For weak coupling, the instability appears to result in a robust breathing of the relevant waveforms
Interlaced solitons and vortices in coupled DNLS lattices
In the present work, we propose a new set of coherent structures that arise
in nonlinear dynamical lattices with more than one components, namely
interlaced solitons. These are waveforms in which in the relevant
anti-continuum limit, i.e. when the sites are uncoupled, one component has
support where the other component does not. We illustrate systematically how
one can combine dynamically stable unary patterns to create ones such for the
binary case of two-components. In the one-dimensional setting, we provide also
a detailed theoretical analysis of the existence and stability of these
waveforms, while in higher dimensions, where such analytical computations are
far more involved, we resort to corresponding numerical computations. Lastly,
we perform direct numerical simulations to showcase how these structures break
up, when exponentially or oscillatorily unstable, to structures with a smaller
number of participating sites.Comment: 11 pages, 10 figure
Bright Discrete Solitons in Spatially Modulated DNLS Systems
In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the “extended” solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Finally, the dynamics also reveal a tendency of the solution profiles to broaden, in line with the above findings. These results pave the way for further explorations of such states in discrete systems, including in higher dimensional settings
Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice
We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring
a defocusing segment, a focusing segment and a transitional interface between
the two. We illustrate that such inhomogeneous settings present vastly
different dynamical behavior than the one expected in their homogeneous
counterparts in the vicinity of the interface. We analyze the relevant
stationary states, as well as their stability by means of perturbation theory
and linear stability analysis. We find good agreement with the numerical
findings in the vicinity of the anti-continuum limit. For larger values of the
coupling, we follow the relevant branches numerically and show that they
terminate at values of the coupling strength which are larger for more extended
solutions. The dynamical development of relevant instabilities is also
monitored in the case of unstable solutions.Comment: 14 pages, 4 figure
Surface Solitons in Three Dimensions
We study localized modes on the surface of a three-dimensional dynamical
lattice. The stability of these structures on the surface is investigated and
compared to that in the bulk of the lattice. Typically, the surface makes the
stability region larger, an extreme example of that being the three-site
"horseshoe"-shaped structure, which is always unstable in the bulk, while at
the surface it is stable near the anti-continuum limit. We also examine effects
of the surface on lattice vortices. For the vortex placed parallel to the
surface this increased stability region feature is also observed, while the
vortex cannot exist in a state normal to the surface. More sophisticated
localized dynamical structures, such as five-site horseshoes and pyramids, are
also considered.Comment: 10 pages, 12 figures, submitted to Phys. Rev.
Bose-Hubbard model with occupation dependent parameters
We study the ground-state properties of ultracold bosons in an optical
lattice in the regime of strong interactions. The system is described by a
non-standard Bose-Hubbard model with both occupation-dependent tunneling and
on-site interaction. We find that for sufficiently strong coupling the system
features a phase-transition from a Mott insulator with one particle per site to
a superfluid of spatially extended particle pairs living on top of the Mott
background -- instead of the usual transition to a superfluid of single
particles/holes. Increasing the interaction further, a superfluid of particle
pairs localized on a single site (rather than being extended) on top of the
Mott background appears. This happens at the same interaction strength where
the Mott-insulator phase with 2 particles per site is destroyed completely by
particle-hole fluctuations for arbitrarily small tunneling. In another regime,
characterized by weak interaction, but high occupation numbers, we observe a
dynamical instability in the superfluid excitation spectrum. The new ground
state is a superfluid, forming a 2D slab, localized along one spatial direction
that is spontaneously chosen.Comment: 16 pages, 4 figure
Asymmetric Line Profiles in Dense Molecular Clumps Observed in MALT90: Evidence for Global Collapse
Using molecular line data from the Millimetre Astronomy Legacy Team 90 GHz Survey (MALT90), we have searched the optically thick \hcop\, line for the "blue asymmetry" spectroscopic signature of infall motion in a large sample of high-mass, dense molecular clumps observed to be at different evolutionary stages of star cluster formation according to their mid-infrared appearance. To quantify the degree of the line asymmetry, we measure the asymmetry parameter , the fraction of the integrated intensity that lies to the blueshifted side of the systemic velocity determined from the optically thin tracer \nthp. For a sample of 1,093 sources, both the mean and median of are positive ( and , respectively) with high statistical significance, and a majority of sources (a fraction of of the sample) show positive values of A, indicating a preponderance of blue-asymmetric profiles over red-asymmetric profiles. Two other measures, the local slope of the line at the systemic velocity and the parameter of \citet{Mardones1997}, also show an overall blue asymmetry for the sample, but with smaller statistical significance. This blue asymmetry indicates that these high-mass clumps are predominantly undergoing gravitational collapse. The blue asymmetry is larger () for the earliest evolutionary stages (quiescent, protostellar and compact H II region) than for the later H II region () and PDR () classifications
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Statics and dynamics of an inhomogeneously nonlinear lattice
We introduce an inhomogeneously nonlinear Schrödinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior in the vicinity of the interface than the one expected in their homogeneous counterparts. We analyze the relevant stationary states, as well as their stability, by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anticontinuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions