Fermion self-trapping in the optical geometry of Einstein-Dirac solitons

Funding: St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1 (P.E.D.L).We analyze gravitationally localized states of multiple fermions with high angular momenta, in the formalism introduced by Finster, Smoller, and Yau [Phys Rev. D 59, 104020 (1999)]. We show that the resulting solitonlike wave functions can be naturally interpreted in terms of a form of self-trapping, where the fermions become localized on shells the locations of which correspond to those of “bulges” in the optical geometry created by their own energy density.Publisher PDFPeer reviewe

Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons

Funding: P. E. D. L. acknowledges funding from a St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1.We present an analysis of excited-state solutions for a gravitationally localized system consisting of a filled shell of high-angular-momentum fermions, using the Einstein-Dirac formalism introduced by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)]. We show that, even when the particle number is relatively low (Nf ≥ 6), the increased nonlinearity in the system causes a significant deviation in behavior from the two-fermion case. Excited-state solutions can no longer be uniquely identified by the value of their central redshift, with this multiplicity producing distortions in the characteristic spiraling forms of the mass-radius relations. We discuss the connection between this effect and the internal structure of solutions in the relativistic regime.Publisher PDFPeer reviewe

Differential approximation for Kelvin-wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency $\omega^* \sim (\epsilon^3 c_s^{20} / \kappa^{16})^{1/13}$ where $\epsilon$ is the total energy injection rate, $c_s$ is the speed of sound and $\kappa$ is the quantum of circulation.Comment: Prepared of publication in JETP Letter

Modeling Kelvin wave cascades in superfluid helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM

Solution to the twin image problem in holography

While the invention of holography by Dennis Gabor truly constitutes an ingenious concept, it has ever since been troubled by the so called twin image problem limiting the information that can be obtained from a holographic record. Due to symmetry reasons there are always two images appearing in the reconstruction process. Thus, the reconstructed object is obscured by its unwanted out of focus twin image. Especially for emission electron as well as for x- and gamma-ray holography, where the source-object distances are small, the reconstructed images of atoms are very close to their twin images from which they can hardly be distinguished. In some particular instances only, experimental efforts could remove the twin images. More recently, numerical methods to diminish the effect of the twin image have been proposed but are limited to purely absorbing objects failing to account for phase shifts caused by the object. Here we show a universal method to reconstruct a hologram completely free of twin images disturbance while no assumptions about the object need to be imposed. Both, amplitude and true phase distributions are retrieved without distortion

Predictability in Systems with Many Characteristic Times: The Case of Turbulence

In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds number. This result could seem in contrast with phenomenological arguments suggesting that, as a consequence of `physical' perturbations, the predictability time is roughly given by the characteristic life-time of the large scale structures, and hence independent of the Reynolds number. We show that such a situation is present in generic systems with many degrees of freedom, since the growth of a non-infinitesimal perturbation is determined by cumulative effects of many different characteristic times and is unrelated to the maximum Lyapunov exponent. Our results are illustrated in a chain of coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed with uufile

Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times