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We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation
Control of noise-induced oscillations of a pendulum with a rondomly vibrating suspension axis
(1997)
The pendant drop technique was used to determine p/A isotherms of docosanic acid spread on the drop surface of an aqueous polymer solution. Two water soluble polymers were used, poly(dimethyl-diallyl-ammoniumchloride) and sodium poly(styrene sulfonate-b-ethylethylene). By fast changes of the drop volume, the monolayers were compressed and dilated. The stress relaxation was monitored and surface rheological dilation parameters were obtained. It is shown that the fatty acid monolayer can be mechanically stabilized by both interacting anionic and cationic polymers. In the case of the anionic polymer, the interaction becomes more pronounced in the presence of salts in the subphase (counterions). Brewster angle microscopy shows that the typical tilt-orientation of crystalline domains of the fatty acid monolayers transforms into a more uniform and fluid-like structure caused by the polymer/monolayer interaction. The surface rheological behavior is dramatically influenced by the polymer binding. The interaction results in surface dilational viscoelastic properties and show that there is a strong resistance against expansion of the complex fatty acid/polymer layer.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from theenvironment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of thegrand- canonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau-Ginzburg functional which - despite the non- interacting nature of the system - displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is base on the grand-canonical ensemble. We show that for an ideal Bose gas neither are the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.
We discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grand-canonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett.(1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales delta n0 proportional to [T/Tc]r Ns with scaling exponents r=3/2, s=1/2 for the 3D harmonic oscillator trapping potential, and r=1, s=2/3 for the 3D box. We derive an explicit expression for r and s in terms of spatial dimension D and spectral index sigma of the single- particle energy spectrum. Our predictions also apply to systems where Bose-Einstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence.
Beziehungen zwischen Texturen und Molekülpackung in Monoschichten an der Luft/Wasser-Grenzfläche
(1997)
Weak gravitational lensing by large-scale structure affects the determination of the cosmological deceleration parameter q0. We find that the lensing induced dispersions on truly standard candles are 0.04 and 0.02 mag at redshift z = 1 and z = 0.5, respectively, in a COBE-normalized cold dark matter universe with Omega 0 = 0.40, Lamda 0 = 0.6, H = 65 km s-1 Mpc-1, and sigma 8 = 0.79. It is shown that one would observe q0 = -0.395^{+0.125}_{-0.095} and q0 = - 0.398^{+0.048}_{-0.077} (the error bars are 2 sigma limits) with standard candles with zero intrinsic dispersion at redshift z = 1 and z = 0.5, respectively, compared to the truth of q0 = -0.400. A standard COBE normalized Omega 0 = 1 CDM model would produce three times as much variance and a mixed (hot and cold) dark matter model would lead to an intermediate result. One unique signature of this dispersion effect is its non-Gaussianity. Although the lensing induced dispersion at lower redshift is still significantly smaller than the currently best observed (total) dispersion of 0.12 mag in a sample of type Ia supernovae, selected with the multicolor light curve shape method, it becomes significant at higher redshift. We show that there is an optimal redshift, in the range z ~ 0.5--2.0 depending on the amplitude of the intrinsic dispersion of the standard candles, at which q0 can be most accurately determined.
Reconstruction of nonlinear time delay models from data by the use of optimal transformations
(1997)
Jumps in quantum theory
(1997)
In this paper we review the discussion about quantum jumps. We sketch the historical background before we present the recent revival of this problem originating in the field of atomic investigations. We present both the theoretical methods and their motivations, the relevance to experiments and an attempt at a preliminary discussion of the role of these developments in our fundamental understanding of quantum physics.
Langmuir-Blodgett films of zinc 11,18,25-tri(tert-butyl)-4-sulfo-phthalocyanine (ZNPctSO3Na) have been deposited onto hydrophilic and hydrophobic silicon wafers. Y-type films were formed on both types of substrate, and the transfer ratio was very close to unity. The organization of the films on the molecular level was probed by X-ray specular reflectivity.
The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfvén velocity) are raised from small values, two-dimensional perturbations become unstable first.
The usage of nonlinear Galerkin methods for the numerical solution of partial differential equations is demonstrated by treating an example. We desribe the implementation of a nonlinear Galerkin method based on an approximate inertial manifold for the 3D magnetohydrodynamic equations and compare its efficiency with the linear Galerkin approximation. Special bifurcation points, time-averaged values of energy and enstrophy as well as Kaplan-Yorke dimensions are calculated for both schemes in order to estimate the number of modes necessary to correctly describe the behavior of the exact solutions.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.