706 research outputs found
Barrier transmission for the one-dimensional nonlinear Schr\"odinger equation: resonances and transmission profiles
The stationary nonlinear Schr\"odinger equation (or Gross-Pitaevskii
equation) for one-dimensional potential scattering is studied. The nonlinear
transmission function shows a distorted profile, which differs from the
Lorentzian one found in the linear case. This nonlinear profile function is
analyzed and related to Siegert type complex resonances. It is shown, that the
characteristic nonlinear profile function can be conveniently described in
terms of skeleton functions depending on a few instructive parameters. These
skeleton functions also determine the decay behavior of the underlying
resonance state. Furthermore we extend the Siegert method for calculating
resonances, which provides a convenient recipe for calculating nonlinear
resonances. Applications to a double Gaussian barrier and a square well
potential illustrate our analysis.Comment: 9 pages, 6 figures, 1 tabl
Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential
The resonance states and the decay dynamics of the nonlinear Schr\"odinger
(or Gross-Pitaevskii) equation are studied for a simple, however flexible model
system, the double delta-shell potential. This model allows analytical
solutions and provides insight into the influence of the nonlinearity on the
decay dynamics. The bifurcation scenario of the resonance states is discussed,
as well as their dynamical stability properties. A discrete approximation using
a biorthogonal basis is suggested which allows an accurate description even for
only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure
Barrier transmission for the Nonlinear Schr\"odinger Equation: Surprises of nonlinear transport
In this communication we report on a peculiar property of barrier
transmission that systems governed by the nonlinear Schroedinger equation share
with the linear one: For unit transmission the potential can be divided at an
arbitrary point into two sub-potentials, a left and a right one, which have
exactly the same transmission. This is a rare case of an exact property of a
nonlinear wave function which will be of interest, e.g., for studies of
coherent transport of Bose-Einstein condensates through mesoscopic waveguideComment: 7 pages, 2 figure
Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
We study the tunneling decay of a Bose-Einstein condensate out of tilted
optical lattices within the mean-field approximation. We introduce a novel
method to calculate also excited resonance eigenstates of the Gross-Pitaevskii
equation, based on a grid relaxation procedure with complex absorbing
potentials. This algorithm works efficiently in a wide range of parameters
where established methods fail. It allows us to study the effects of the
nonlinearity in detail in the regime of resonant tunneling, where the decay
rate is enhanced by resonant coupling to excited unstable states.Comment: Revised and enlarged version, including 1 additional figur
Hamiltonian chaos in a coupled BEC -- optomechanical cavity system
We study a hybrid optomechanical system consisting of a Bose-Einstein
condensate (BEC) trapped inside a single-mode optical cavity with a moving
end-mirror. The intracavity light field has a dual role: it excites a momentum
side-mode of the condensate, and acts as a nonlinear spring that couples the
vibrating mirror to that collective density excitation. We present the dynamics
in a regime where the intracavity optical field, the mirror, and the side-mode
excitation all display bistable behavior. In this regime we find that the
dynamics of the system exhibits Hamiltonian chaos for appropriate initial
conditions.Comment: 5 figure
A purely reflective large wide-field telescope
Two versions of a fast, purely reflective Paul-Baker type telescope are
discussed, each with an 8.4-m aperture, 3 deg diameter flat field and f/1.25
focal ratio.
The first version is based on a common, even asphere type of surface with
zero conic constant. The primary and tertiary mirrors are 6th order aspheres,
while the secondary mirror is an 8th order asphere (referred to here for
brevity, as the 6/8/6 configuration). The D_80 diameter of a star image varies
from 0''.18 on the optical axis up to 0''.27 at the edge of the field (9.3-13.5
mcm).
The second version of the telescope is based on a polysag surface type which
uses a polynomial expansion in the sag z, r^2 = 2R_0z - (1+b)z^2 + a_3 z^3 +
a_4 z^4 + ... + a_N z^N, instead of the common form of an aspheric surface.
This approach results in somewhat better images, with D_80 ranging from 0''.16
to 0''.23, using a lower-order 3/4/3 combination of powers for the mirror
surfaces. An additional example with 3.5-m aperture, 3.5 deg diameter flat
field, and f/1.25 focal ratio featuring near-diffraction-limited image quality
is also presented.Comment: 14 pages, 6 figures; new examples adde
Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling
In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well
potential can be described by a many particle Hamiltonian of Bose-Hubbard type.
We focus on such a BEC whose interatomic interaction strength is modulated
periodically by -kicks which represents a realization of a kicked top.
In the (classical) mean-field approximation it provides a rich mixed phase
space dynamics with regular and chaotic regions. By increasing the
kick-strength a bifurcation leads to the appearance of self-trapping states
localized on regular islands. This self-trapping is also found for the many
particle system, however in general suppressed by coherent many particle
tunneling oscillations. The tunneling time can be calculated from the
quasi-energy splitting of the corresponding Floquet states. By varying the
kick-strength these quasi-energy levels undergo both avoided and even actual
crossings. Therefore stimulation or complete destruction of tunneling can be
observed for this many particle system
Interaction-induced decoherence in non-Hermitian quantum walks of ultracold Bosons
We study the influence of particle interaction on a quantum walk on a
bipartite one-dimensional lattice with decay from every second site. The
corresponding non-interacting (linear) system has been shown to have a
topological transition described by the average displacement before decay. Here
we use this topological quantity to distinguish coherent quantum dynamics from
incoherent classical dynamics caused by a breaking of the translational
symmetry. We furthermore analyze the behavior by means of a rate equation
providing a quantitative description of the incoherent nonlinear dynamics.Comment: Revised and extended version, 5 pages, 5 figure
Evidence for a Single-Spin Azimuthal Asymmetry in Semi-inclusive Pion Electroproduction
Single-spin asymmetries for semi-inclusive pion production in deep-inelastic scattering have been measured for the first time. A significant target-spin asymmetry of the distribution in the azimuthal angle φ of the pion relative to the lepton scattering plane was formed for π^+ electroproduction on a longitudinally polarized hydrogen target. The corresponding analyzing power in the sinφ moment of the cross section is 0.022±0.005±0.003. This result can be interpreted as the effect of terms in the cross section involving chiral-odd spin distribution functions in combination with a chiral-odd fragmentation function that is sensitive to the transverse polarization of the fragmenting quark
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