127 research outputs found
Dynamics of nonlinear excitations of helically confined charges
We explore the long-time dynamics of a system of identical charged particles
trapped on a closed helix. This system has recently been found to exhibit an
unconventional deformation of the linear spectrum when tuning the helix radius.
Here we show that the same geometrical parameter can affect significantly also
the dynamical behaviour of an initially broad excitation for long times. In
particular, for small values of the radius, the excitation disperses into the
whole crystal whereas within a specific narrow regime of larger radii the
excitation self-focuses, assuming finally a localized form. Beyond this regime,
the excitation defocuses and the dispersion gradually increases again. We
analyze this geometrically controlled nonlinear behaviour using an effective
discrete nonlinear Schr\"{o}dinger model, which allows us among others to
identify a number of breather-like excitations.Comment: 11 pages, 7 figure
Classical scattering of charged particles confined on an inhomogeneous helix
We explore the effects arising due to the coupling of the center of mass and
relative motion of two charged particles confined on an inhomogeneous helix
with a locally modified radius. It is first proven that a separation of the
center of mass and the relative motion is provided if and only if the confining
manifold represents a homogeneous helix. In this case bound states of
repulsively Coulomb interacting particles occur. For an inhomogeneous helix,
the coupling of the center of mass and relative motion induces an energy
transfer between the collective and relative motion, leading to dissociation of
initially bound states in a scattering process. Due to the time reversal
symmetry, a binding of the particles out of the scattering continuum is thus
equally possible. We identify the regimes of dissociation for different initial
conditions and provide an analysis of the underlying phase space via Poincar\'e
surfaces of section. Bound states inside the inhomogeneity as well as resonant
states are identified.Comment: 15 pages, 18 figure
Vortex-Bright Soliton Dipoles: Bifurcations, Symmetry Breaking and Soliton Tunneling in a Vortex-Induced Double Well
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein
condensates through bifurcations from suitable eigenstates of the underlying
linear system is examined. These dipoles can have their bright solitary
structures be in phase (symmetric) or out of phase (anti-symmetric). The
dynamical robustness of each of these two possibilities is considered and the
out-of-phase case is found to exhibit an intriguing symmetry-breaking
instability that can in turn lead to tunneling of the bright wavefunction
between the two vortex "wells". We interpret this phenomenon by virtue of a
vortex-induced double well system, whose spontaneous symmetry breaking leads to
asymmetric vortex-bright dipoles, in addition to the symmetric and
anti-symmetric ones. The theoretical prediction of these states is corroborated
by detailed numerical computations.Comment: 14 pages, 8 figure
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