763 research outputs found
Performance analysis of grazing incidence imaging systems
An exact expression relating the coordinates of a point on the incident ray, a point of reflection from an arbitrary surface, and a point on the reflected ray is derived. The exact relation is then specialized for the case of grazing incidence, and first order and third order systematic analyses are carried out for a single reflective surface and then for a combination of two surfaces. The third order treatment yields a complete set of primary aberrations for single element and two element systems. The importance of a judicious choice for a coordinate system in showing field curvature to clearly be the predominant aberration for a two element system is discussed. The validity of the theory is verified through comparisons with the exact ray trace results for the case of the telescope
Experimental evaluation of the ring focus test for X-ray telescopes using AXAF's technology mirror assembly, MSFC CDDF Project No. H20
A test method particularly suited for X-ray telescopes was evaluated experimentally. The method makes use of a focused ring formed by an annular aperture when using a point source at a finite distance. This would supplement measurements of the best focus image which is blurred when the test source is at a finite distance. The telescope used was the Technology Mirror Assembly of the Advanced X-ray Astrophysis Facility (AXAF) program. Observed ring image defects could be related to the azimuthal location of their sources in the telescope even though in this case the predicted sharp ring was obscured by scattering, finite source size, and residual figure errors
Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
Bosonic quantum conversion systems can be modeled by many-particle
single-mode Hamiltonians describing a conversion of molecules of type A
into molecules of type B and vice versa. These Hamiltonians are analyzed in
terms of generators of a polynomially deformed algebra. In the
mean-field limit of large particle numbers, these systems become classical and
their Hamiltonian dynamics can again be described by polynomial deformations of
a Lie algebra, where quantum commutators are replaced by Poisson brackets. The
Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres
with cusp singularities depending on and . It is demonstrated that the
many-particle eigenvalues can be recovered from the mean-field dynamics using a
WKB type quantization condition. The many-particle state densities can be
semiclassically approximated by the time-periods of periodic orbits, which show
characteristic steps and singularities related to the fixed points, whose
bifurcation properties are analyzed.Comment: 13 pages, 13 figure
Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
Many features of Bloch oscillations in one-dimensional quantum lattices with
a static force can be described by quasiclassical considerations for example by
means of the acceleration theorem, at least for Hermitian systems. Here the
quasiclassical approach is extended to non-Hermitian lattices, which are of
increasing interest. The analysis is based on a generalised non-Hermitian phase
space dynamics developed recently. Applications to a single-band tight-binding
system demonstrate that many features of the quantum dynamics can be understood
from this classical description qualitatively and even quantitatively. Two
non-Hermitian and -symmetric examples are studied, a Hatano-Nelson lattice
with real coupling constants and a system with purely imaginary couplings, both
for initially localised states in space or in momentum. It is shown that the
time-evolution of the norm of the wave packet and the expectation values of
position and momentum can be described in a classical picture.Comment: 20 pages, 8 figures, typos corrected, slightly extended, accepted for
publication in New Journal of Physics in Focus Issue on Parity-Time Symmetry
in Optics and Photonic
Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
We investigate an -particle Bose-Hubbard dimer with an additional
effective decay term in one of the sites. A mean-field approximation for this
non-Hermitian many-particle system is derived, based on a coherent state
approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in
particular the fixed point structures showing characteristic modifications of
the self-trapping transition, are analyzed. The mean-field dynamics is found to
be in reasonable agreement with the full many-particle evolution.Comment: 4 pages, 3 figures, published versio
Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances
We study the properties of coupled linear and nonlinear resonances. The
fundamental phenomena and the level crossing scenarios are introduced for a
nonlinear two-level system with one decaying state, describing the dynamics of
a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or
nonlinear Schroedinger equation). An important application of the discussed
concepts is the dynamics of a condensate in tilted optical lattices. In
particular the properties of resonance eigenstates in double-periodic lattices
are discussed, in the linear case as well as within mean-field theory. The
decay is strongly altered, if an additional period-doubled lattice is
introduced. Our analytic study is supported by numerical computations of
nonlinear resonance states, and future applications of our findings for
experiments with ultracold atoms are discussed.Comment: 12 pages, 17 figure
Test method for telescopes using a point source at a finite distance
A test method for telescopes that makes use of a focused ring formed by an annular aperture when using a point source at a finite distance is evaluated theoretically and experimentally. The results show that the concept can be applied to near-normal, as well as grazing incidence. It is particularly suited for X-ray telescopes because of their intrinsically narrow annular apertures, and because of the largely reduced diffraction effects
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
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
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