Discrete Wigner functions and quantum computational speedup

In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.Comment: 7 pages, 2 figures, RevTeX. v2: clarified discussion on dynamics, added refs., published versio

The Energy Spectrum of Primary Cosmic Ray Electrons in Clusters of Galaxies and Inverse Compton Emission

Models for the evolution of the integrated energy spectrum of primary cosmic ray electrons in clusters of galaxies have been calculated, including the effects of losses due to inverse Compton (IC), synchrotron, and bremsstrahlung emission, and Coulomb losses to the intracluster medium (ICM). The combined time scale for these losses reaches a maximum of ~3e9 yr for electrons with a Lorentz factor ~300. Only clusters in which there has been a substantial injection of relativistic electrons since z <~ 1 will have any significant population of primary cosmic ray electrons at present. In typical models, there is a broad peak in the electron energy distribution extending to gamma~300, and a steep drop in the electron population beyond this. In clusters with current particle injection, there is a power-law tail of higher energy electrons with an abundance determined by the current rate of injection. A significant population of electrons with gamma~300, associated with the peak in the particle loss time, is a generic feature of the models. The IC and synchrotron emission from these models was calculated. In the models, EUV and soft X-ray emission are nearly ubiquitous. This emission is produced by electrons with gamma~300. The spectra are predicted to drop rapidly in going from the EUV to the X-ray band. The IC emission also extends down the UV, optical, and IR bands with a fairly flat spectrum. Hard X-ray (HXR) and diffuse radio emission due to high energy electrons (gamma~10e4) is present only in clusters which have current particle acceleration. Assuming that the electrons are accelerated in ICM shocks, one would only expect diffuse HXR/radio emission in clusters which are currently undergoing a large merger.Comment: Accepted for publication in the Astrophysical Journal, with minor revisons to wording for clarity and one additional reference. 19 pages with 16 embedded Postscript figures in emulateapj.sty. Abbreviated abstract belo

Composition profiles of InAs–GaAs quantum dots determined by medium-energy ion scattering

The composition profile along the [001] growth direction of low-growth-rate InAs–GaAs quantum dots (QDs) has been determined using medium-energy ion scattering (MEIS). A linear profile of In concentration from 100% In at the top of the QDs to 20% at their base provides the best fit to MEIS energy spectra

Discovery of Two High-Magnetic-Field Radio Pulsars

We report the discovery of two young isolated radio pulsars with very high inferred magnetic fields. PSR J1119-6127 has period P = 0.407 s, and the largest period derivative known among radio pulsars, Pdot = 4.0e-12. Under standard assumptions these parameters imply a characteristic spin-down age of only tau = 1.6 kyr and a surface dipole magnetic field strength of B = 4.1e13 G. We have measured a stationary period-second-derivative for this pulsar, resulting in a braking index of n = 2.91+-0.05. We have also observed a glitch in the rotation of the pulsar, with fractional period change Delta_P/P = -4.4e-9. Archival radio imaging data suggest the presence of a previously uncataloged supernova remnant centered on the pulsar. The second pulsar, PSR J1814-1744, has P = 3.975 s and Pdot = 7.4e-13. These parameters imply tau = 85 kyr, and B = 5.5e13 G, the largest of any known radio pulsar. Both PSR J1119-6127 and PSR J1814-1744 show apparently normal radio emission in a regime of magnetic field strength where some models predict that no emission should occur. Also, PSR J1814-1744 has spin parameters similar to the anomalous X-ray pulsar (AXP) 1E 2259+586, but shows no discernible X-ray emission. If AXPs are isolated, high magnetic field neutron stars (``magnetars''), these results suggest that their unusual attributes are unlikely to be merely a consequence of their very high inferred magnetic fields.Comment: 7 pages, 3 embedded EPS figures, to be published in Ap

Short range correlations in relativistic nuclear matter models

Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. It is shown that the correlations give rise to an extra node in the ground-state wave-function in the nucleons, contrary to what happens in non-relativistic calculations with a hard core. The effect of the correlations in the ground state properties of the nuclear matter and neutron matter is studied. The nucleon effective mass and equation of state (EOS) are very sensitive to short range correlations. In particular, if the pion contact term is neglected a softening of the EOS is predicted. Correlations have also an important effect on the neutron matter EOS which presents no binding but only a very shallow minimum contrary to the Walecka model.Comment: 8pages, 4 figure

C and N Abundances in Stars At the Base of the Red Giant Branch in M5

We present an analysis of a large sample of moderate resolution Keck LRIS spectra of subgiant (V \sim 17.2) and fainter stars in the Galactic globular cluster M5 (NGC 5904) with the goal of deriving C and N abundances. Star-to-star stochastic variations with significant range in both [C/Fe] and [N/Fe] are found at all luminosities extending to the bottom of the RGB at M_V \sim +3. Similar variations in CH appear to be present in the main sequence turnoff spectra. There is no sign of a change in the behavior of C and N with evolutionary stage over the full range in luminosity of the RGB and SGB. The C and N abundances appear strongly anti-correlated, as would be expected from the CN-cycle processing of stellar material. Yet the present stars are considerably fainter than the RGB bump, the point at which deep mixing is believed to set in. On this basis, while the observed abundance pattern is consistent with proton capture nucleosynthesis, we infer that the site of the reactions is likely not within the present sample, but rather in a population of more massive (2 -- 5 M(Sun)) now defunct stars. The range of variation of the N abundances is very large and the sum of C+N increases as C decreases. To reproduce this requires the incorporation not only of CN but also of ON-processed material. Furthermore, the existence of this correlation is quite difficult to reproduce with an external mechanism such as ``pollution'' with material processed in a more massive AGB star, which mechanism is fundamentally stochastic in nature. We therefore suggest that although the internal mixing hypothesis has serious flaws,new theoretical insights are needed and it should not be ruled out yet. (abridged)Comment: Slightly updated version to conform to that accepted by the A

The origin of phase in the interference of Bose-Einstein condensates

We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a so-called condensate wave functions having a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state, for which the particle number is uncertain, but phase is known. However, how one would prepare such a state before an experiment is not obvious. We show that a phase can also arise from experiments using condensates in Fock states, that is, having known particle numbers. Analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of ``spontaneously broken gauge symmetry'' and to ``hidden variables'' is mentioned.Comment: 22 pages 4 figure

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic

Ensemble inequivalence in systems with long-range interactions

Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We further show that a broad class of systems with non-integrable interactions are indeed of mean-field type in the sense specified, so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble.Comment: 12 pages, no figure

Cygnus X-3 in outburst : quenched radio emission, radiation losses and variable local opacity

We present multiwavelength observations of Cygnus X-3 during an extended outburst in 1994 February - March. Intensive radio monitoring at 13.3, 3.6 & 2.0 cm is complemented by observations at (sub)millimetre and infrared wavelengths, which find Cyg X-3 to be unusually bright and variable, and include the first reported detection of the source at 0.45 mm. We report the first confirmation of quenched radio emission prior to radio flaring independent of observations at Green Bank. The observations reveal evidence for wavelength-dependent radiation losses and gradually decreasing opacity in the environment of the radio jet. We find that the radiation losses are likely to be predominantly inverse Compton losses experienced by the radio-emitting electrons in the strong radiation field of a luminous companion to the compact object. We interpret the decreasing opacity during the flare sequence as resulting from a decreasing proportion of thermal electrons entrained in the jet, reflecting a decreasing density in the region of jet formation. We present, drawing in part on the work of other authors, a model based upon mass-transfer rate instability predicting gamma-ray, X-ray, infrared and radio trends during a radio flaring sequence.Comment: LaTeX, 11 pages, 6 figures. Submitted to MNRA