673 research outputs found
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
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
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
Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein
condensate in a tilted optical lattice is studied in a discrete mean-field
approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation.
If the static field is varied the system shows a plethora of dynamical
phenomena. In the strong field limit we demonstrate the existence of (almost)
non-spreading states which remain localized on the lattice region populated
initially and show coherent Bloch oscillations with fractional revivals in the
momentum space (so called quantum carpets). With decreasing field, the dynamics
becomes irregular, however, still confined in configuration space. For even
weaker fields we find sub-diffusive dynamics with a wave-packet width spreading
as .Comment: 4 pages, 5 figure
Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators
We discuss some basic tools for an analysis of one-dimensionalquantum systems
defined on a cyclic coordinate space. The basic features of the generalized
coherent states, the complexifier coherent states are reviewed. These states
are then used to define the corresponding (quasi)densities in phase space. The
properties of these generalized Husimi distributions are discussed, in
particular their zeros.Furthermore, the use of the complexifier coherent states
for a semiclassical analysis is demonstrated by deriving a semiclassical
coherent state propagator in phase space.Comment: 29 page
Chaotic Evolution in Quantum Mechanics
A quantum system is described, whose wave function has a complexity which
increases exponentially with time. Namely, for any fixed orthonormal basis, the
number of components required for an accurate representation of the wave
function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure
Evolution of Liouville density of a chaotic system
An area-preserving map of the unit sphere, consisting of alternating twists
and turns, is mostly chaotic. A Liouville density on that sphere is specified
by means of its expansion into spherical harmonics. That expansion initially
necessitates only a finite number of basis functions. As the dynamical mapping
proceeds, it is found that the number of non-negligible coefficients increases
exponentially with the number of steps. This is to be contrasted with the
behavior of a Schr\"odinger wave function which requires, for the analogous
quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB +
2 kB + 1 kB + 4 kB
A Rapid Screening Psychometric Test
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66666/2/10.1177_000992286900800506.pd
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