Instanton Approach to Josephson Tunneling between Trapped Condensates

An instanton method is proposed to investigate the quantum tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. We point out some intrinsic pathologies in the earlier treatments of other authors and make an effort to go beyond these very simple zero order models. The tunneling amplitude may be calculated in the Thomas-Fermi approximation and beyond it; we find it depends on the number of the trapped atoms, through the chemical potential. Some suggestions are given for the observation of the Josephson oscillation and the MQST.Comment: 20 pages, Revtex4, 6 figures. Abbreviated version accepted by Eur. Phys. J

Testing Lorentz invariance by use of vacuum and matter filled cavity resonators

We consider tests of Lorentz invariance for the photon and fermion sector that use vacuum and matter-filled cavities. Assumptions on the wave-function of the electrons in crystals are eliminated from the underlying theory and accurate sensitivity coefficients (including some exceptionally large ones) are calculated for various materials. We derive the Lorentz-violating shift in the index of refraction n, which leads to additional sensitivity for matter-filled cavities ; and to birefringence in initially isotropic media. Using published experimental data, we obtain improved bounds on Lorentz violation for photons and electrons at levels of 10^-15 and below. We discuss implications for future experiments and propose a new Michelson-Morley type experiment based on birefringence in matter.Comment: 15 pages, 8 table

“Though this be madness, yet there is method in’t.” A counterfactual analysis of Richard Wagner’s Tannhäuser

Much like Wagner himself, the eponymous hero of Tannhäuser treads a path of stark contrasts and rapid swings. From Wartburg to the Venusberg and to the Vatican, the gifted bard transforms from self-centered artist to seduced disciple, disillusioned devotee, hopeful lover, self-loathing pilgrim and finally redeemed martyr. He tries everything and everything is trying. These contrasts reach a peak in the opera‟s central episode, the song contest at Wartburg. Tannhäuser has just been welcomed at the court, received Elisabeth‟s favor and affection, and is ready to compete for the contest‟s prize, one as lofty as possibly the princess‟ hand. Instead of securing his reintegration to Wartburg with a brilliant performance, however, he spoils the event with insolent remarks and the exhibitionist disclosure of his Venusberg experience. His behavior offends his peers, scandalizes the court, breaks Elisabeth‟s heart, and brings him to the edge of death. Why would Tannhäuser sacrifice everything for nothing

Faraday waves on a viscoelastic liquid

We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external drive competes with the usual subharmonic Faraday instability. Close to the bicriticality the nonlinear wave interaction gives rise to a variety of novel surface states: Localised patches of hexagons, hexagonal superlattices, coexistence of hexagons and lines. Theoretical stability calculations and qualitative resonance arguments support the experimental observations.Comment: 4 pages, 4figure

Once again: Instanton method vs. WKB

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam${\acute e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lam${\acute e}$ potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.Comment: 10 pages, no figures. References list revised according to JHE

Lagrangian Statistics of Navier-Stokes- and MHD-Turbulence

We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to $1024^3$ collocation points and 10 million particles in the Navier-Stokes case and $512^3$ collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. [1] and Xu et al. [2]. They differ from the simulations of Biferale et al. [3] due to differences of the ranges choosen for evaluating the structure functions. In Navier-Stokes turbulence intermittency is stronger than predicted by a multifractal approach of [3] whereas in MHD turbulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier-Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. Application of the multifractal approach for the modeling of the acceleration PDFs works well for the Navier-Stokes case but in the MHD case just the tails are well described.Comment: to appear in J. Plasma Phy