Upper Bound on the Capacity of a Cascade of Nonlinear and Noisy Channels

An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schroedinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.Comment: The main change is to define the noise as bandlimited already in (8) rather than before (15). This serves to clarify subsequent step

Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models

NMR evidence for a strong modulation of the Bose-Einstein Condensate in BaCuSi2_2O6_6

We present a $^{63,65}$Cu and $^{29}$Si NMR study of the quasi-2D coupled spin 1/2 dimer compound BaCuSi$_2$O$_6$ in the magnetic field range 13-26 T and at temperatures as low as 50 mK. NMR data in the gapped phase reveal that below 90 K different intra-dimer exchange couplings and different gaps ($\Delta_{\rm{B}}/\Delta_{\rm{A}}$ = 1.16) exist in every second plane along the c-axis, in addition to a planar incommensurate (IC) modulation. $^{29}$Si spectra in the field induced magnetic ordered phase reveal that close to the quantum critical point at $H_{\rm{c1}}$ = 23.35 T the average boson density $\bar{n}$ of the Bose-Einstein condensate is strongly modulated along the c-axis with a density ratio for every second plane $\bar{n}_{\rm{A}}/\bar{n}_{\rm{B}} \simeq 5$. An IC modulation of the local density is also present in each plane. This adds new constraints for the understanding of the 2D value $\phi$ = 1 of the critical exponent describing the phase boundary

Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors

We consider source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, $\xi^a$. We assume further that the electromagnetic field tensor, $F_{ab}$, is invariant under the action of the isometry group induced by $\xi^a$. It is proved that whenever the two potentials associated with the electromagnetic field are functionally independent the entire content of Maxwell's equations is equivalent to the relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation we argue that it is enough to solve merely Einstein's equation for these electrovac spacetimes because the relevant equations of motion will be satisfied automatically. It is also shown that for the exceptional case of functionally related potentials \n^aT_{ab}=0 implies along with one of the relevant equations of motion that the complementary equation concerning the electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+

Changes in Polarization Position Angle across the Eclipse in the Double Pulsar System

We investigate the changes in polarization position angle in radiation from pulsar A around the eclipse in the Double Pulsar system PSR J0737-3039A/B at the 20 cm and 50 cm wavelengths using the Parkes 64-m telescope. The changes are ~2\sigma\ during and shortly after the eclipse at 20 cm but less significant at 50 cm. We show that the changes in position angle during the eclipse can be modelled by differential synchrotron absorption in the eclipse regions. Position angle changes after the eclipse are interpreted as Faraday rotation in the magnetotail of pulsar B. Implied charge densities are consistent with the Goldreich-Julian density, suggesting that the particle energies in the magnetotail are mildly relativistic.Comment: Accepted for publication in The Astrophysical Journal Letter

Information Content in B→VVB \to VV Decays and the Angular Moments Method

The time-dependent angular distributions of decays of neutral $B$ mesons into two vector mesons contain information about the lifetimes, mass differences, strong and weak phases, form factors, and CP violating quantities. A statistical analysis of the information content is performed by giving the ``information'' a quantitative meaning. It is shown that for some parameters of interest, the information content in time and angular measurements combined may be orders of magnitude more than the information from time measurements alone and hence the angular measurements are highly recommended. The method of angular moments is compared with the (maximum) likelihood method to find that it works almost as well in the region of interest for the one-angle distribution. For the complete three-angle distribution, an estimate of possible statistical errors expected on the observables of interest is obtained. It indicates that the three-angle distribution, unraveled by the method of angular moments, would be able to nail down many quantities of interest and will help in pointing unambiguously to new physics.Comment: LaTeX, 34 pages with 9 figure

Spin polarization in a T-shape conductor induced by strong Rashba spin-orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spin-orbit interaction in a T-shaped conductor proposed by A.A. Kiselev and K.W. Kim (Appl. Phys. Lett. {\bf 78} 775 (2001)). The recursive Green function method is used to calculate the three terminal spin dependent transmission probabilities. We focus on single-channel transport and show that the spin polarization becomes nearly 100 % with a conductance close to $e^{2}/h$ for sufficiently strong spin-orbit coupling. This is interpreted by the fact that electrons with opposite spin states are deflected into an opposite terminal by the spin dependent Lorentz force. The influence of the disorder on the predicted effect is also discussed. Cases for multi-channel transport are studied in connection with experiments

The Formation of the Double Pulsar PSR J0737-3039A/B

Recent timing observations of the double pulsar J0737-3039A/B have shown that its transverse velocity is extremely low, only 10 km/s, and nearly in the Plane of the Galaxy. With this new information, we rigorously re-examine the history and formation of this system, determining estimates of the pre-supernova companion mass, supernova kick and misalignment angle between the pre- and post-supernova orbital planes. We find that the progenitor to the recently formed `B' pulsar was probably less than 2 MSun, lending credence to suggestions that this object may not have formed in a normal supernova involving the collapse of an iron core. At the same time, the supernova kick was likely non-zero. A comparison to the history of the double-neutron-star binary B1534+12 suggests a range of possible parameters for the progenitors of these systems, which should be taken into account in future binary population syntheses and in predictions of the rate and spatial distribution of short gamma-ray burst events.Comment: To appear in MNRAS Letters. Title typo fix only; no change to pape

Electrovac pppp-waves

New exact solutions of the Einstein-Maxwell field equations that describe $pp$-waves are presented