Oscillations of dark solitons in trapped Bose-Einstein condensates

We consider a one-dimensional defocusing Gross--Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to radiative losses (sound emission). We develop a systematic asymptotic multi-scale expansion method in the limit when the potential trap is flat. The first-order approximation predicts a uniform frequency of oscillations for the dark soliton of arbitrary amplitude. The second-order approximation predicts the nonlinear growth rate of the oscillation amplitude, which results in decay of the dark soliton. The results are compared with the previous publications and numerical computations.Comment: 13 pages, 3 figure

Transition state theory for wave packet dynamics. II. Thermal decay of Bose-Einstein condensates with long-range interaction

We apply transition state theory to coupled Gaussian wave packets and calculate thermal decay rates of Bose-Einstein condensates with additional long-range interaction. The ground state of such a condensate is metastable if the contact interaction is attractive and a sufficient thermal excitation may lead to its collapse. The use of transition state theory is made possible by describing the condensate within a variational framework and locally mapping the variational parameters to classical phase space as has been demonstrated in the preceding paper [A. Junginger, J. Main, and G. Wunner, submitted to J. Phys. A]. We apply this procedure to Gaussian wave packets and present results for condensates with monopolar 1/r-interaction comparing decay rates obtained by using different numbers of coupled Gaussian trial wave functions as well as different normal form orders.Comment: 14 pages, 4 figures, submitted to J. Phys.

Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary System Perturbed by Gravitational Radiation

The method of averaging is used to investigate the phenomenon of capture into resonance for a model that describes a Keplerian binary system influenced by radiation damping and external normally incident periodic gravitational radiation. The dynamical evolution of the binary orbit while trapped in resonance is elucidated using the second order partially averaged system. This method provides a theoretical framework that can be used to explain the main evolutionary dynamics of a physical system that has been trapped in resonance.Comment: REVTEX Style, Submitte

Transition state theory for wave packet dynamics. I. Thermal decay in metastable Schr\"odinger systems

We demonstrate the application of transition state theory to wave packet dynamics in metastable Schr\"odinger systems which are approached by means of a variational ansatz for the wave function and whose dynamics is described within the framework of a time-dependent variational principle. The application of classical transition state theory, which requires knowledge of a classical Hamilton function, is made possible by mapping the variational parameters to classical phase space coordinates and constructing an appropriate Hamiltonian in action variables. This mapping, which is performed by a normal form expansion of the equations of motion and an additional adaptation to the energy functional, as well as the requirements to the variational ansatz are discussed in detail. The applicability of the procedure is demonstrated for a cubic model potential for which we calculate thermal decay rates of a frozen Gaussian wave function. The decay rate obtained with a narrow trial wave function agrees perfectly with the results using the classical normal form of the corresponding point particle. The results with a broader trial wave function go even beyond the classical approach, i.e., they agree with those using the quantum normal form. The method presented here will be applied to Bose-Einstein condensates in the following paper [A. Junginger, M. Dorwarth, J. Main, and G. Wunner, submitted to J. Phys. A].Comment: 21 pages, 3 figures, submitted to J. Phys.

Experimental Tests of Charge Symmetry Violation in Parton Distributions

Recently, a global phenomenological fit to high energy data has included charge symmetry breaking terms, leading to limits on the allowed magnitude of such effects. We discuss two possible experiments that could search for isospin violation in valence parton distributions. We show that, given the magnitude of charge symmetry violation consistent with existing global data, such experiments might expect to see effects at a level of several percent. Alternatively, such experiments could significantly decrease the upper limits on isospin violation in parton distributions.Comment: 20 pages, 6 figure

A serological investigation of caseous lymphadenitis in four flocks of sheep

A double antibody sandwich ELISA developed by ID-DLO, Lelystad to detect Corynebocterium pseudotuberculosis infection was used on 329 sheep from four pedigree Suffolk flocks in which clinical cases of caseous lymphadenitis (CLA) had occurred. At subsequent necropsy, typical CLA lesions were seen in 133 sheep, and the diagnosis was confirmed on culture. Lesions were most commonly seen in lungs (n = 46), parotid lymph nodes (n = 44), prescapular lymph nodes (n = 38) and mediastinal lymph nodes (n = 31). The sensitivity of the ELISA test for detecting culture-positive sheep was 0.88, while the specificity of the test was 0.55. The antibody ELISA detected 87.5 per cent of sheep that had CLA lesions restricted to internal organs only. It was concluded that the ELISA test has a valuable role in detecting sheep with both clinical and subclinical CLA

Testing Partonic Charge Symmetry at a High-Energy Electron Collider

We examine the possibility that one could measure partonic charge symmetry violation (CSV) by comparing neutrino or antineutrino production through charged-current reactions induced by electrons or positrons at a possible electron collider at the LHC. We calculate the magnitude of CSV that might be expected at such a facility. We show that this is likely to be a several percent effect, substantially larger than the typical CSV effects expected for partonic reactions.Comment: 7 pages, 4 figure

Volume-preserving normal forms of Hopf-zero singularity

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a non-zero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any non-degenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified R\"{o}ssler and generalized Kuramoto--Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple

Solvent response to fluorine-atom reaction dynamics in liquid acetonitrile

Solvent restructuring and vibrational cooling follow exothermic fluorine-atom reactions in acetonitrile.</p