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

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

Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown, that these phenomena are related to a depletion of the Floquet-Bogoliubov states and a decoherence of the condensate in the many-particle description. Three different types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability, and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.Comment: 12 pages, 14 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

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

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 $t^{1/4}$.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

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