Convex Trace Functions on Quantum Channels and the Additivity Conjecture

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are "additive" in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.Comment: 9 pages, 1 figure. Published versio

Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins and investigated in detail by Pendlebury et al. Their analysis was based on the Bloch equations. In subsequent work using the spin density matrix Lamoreaux and Golub showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently we presented a solution of the Schr\"odinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [Steyerl et al.] Here we extend this work to show how the Redfield theory follows directly from the Schr\"odinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., Nicholas et al.] Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and non-stochastic systems and thus we can illustrate the transient spin dynamics, i.e. the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schr\"odinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.Comment: 20 pages, 8 figure

Fundamental Plane Distances to Early-type Field Galaxies in the South Equatorial Strip. I. The Spectroscopic Data

Radial velocities and central velocity dispersions are derived for 238 E/S0 galaxies from medium-resolution spectroscopy. New spectroscopic data have been obtained as part of a study of the Fundamental Plane distances and peculiar motions of early-type galaxies in three selected directions of the South Equatorial Strip, undertaken in order to investigate the reality of large-scale streaming motion; results of this study have been reported in M\"uller $et$ $al.$ (1998). The new APM South Equatorial Strip Catalog ($-17^{\circ}.5 < \delta < +2^{\circ}.5$) was used to select the sample of field galaxies in three directions: (1) 15h10 - 16h10; (2) 20h30 - 21h50; (3) 00h10 - 01h30. The spectra obtained have a median S/N per ${\AA}$ of 23, an instrumental resolution (FWHM) of $\sim$ 4 ${\AA}$, and the spectrograph resolution (dispersion) is $\sim$ 100 km~s$^{-1}$. The Fourier cross-correlation method was used to derive the radial velocities and velocity dispersions. The velocity dispersions have been corrected for the size of the aperture and for the galaxy effective radius. Comparisons of the derived radial velocities with data from the literature show that our values are accurate to 40 km~s$^{-1}$. A comparison with results from J\orgensen et al. (1995) shows that the derived central velocity dispersion have an rms scatter of 0.036 in $\log \sigma$. There is no offset relative to the velocity dispersions of Davies et al. (1987).Comment: accepted for publication in Astronomy & Astrophysics Supplement Serie

Thermal breakdown of coherent backscattering: a case study of quantum duality

We investigate coherent backscattering of light by two harmonically trapped atoms in the light of quantitative quantum duality. Including recoil and Doppler shift close to an optical resonance, we calculate the interference visibility as well as the amount of which-path information, both for zero and finite temperature.Comment: published version with minor changes and an added figur

Inheritance of Isoenzymes in European Beech (Fagus sylvatica L.)

Segregation of isoenzymes was studied among 34 full-sib families of Fagus sylvatica L. by means of gel electrophoresis. Of the 16 enzyme systems analyzed, two showed substantial tissue-specific expression of isoenzymes. The remaining 14 enzyme systems are controlled genetically by at least 20 polymorphic gene loci, three of which were inferred from additional population studies. The inheritance of the complex system of 6PGDH is studied in detail. A 20-locus nomenclature is suggested, including 78 codominant alleles. Analyses of two-locus combinations did not reveal linkage between any of the tested gene loc

On the commutability of homogenization and linearization in finite elasticity

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density

Coherent QED, Giant Resonances and (e+e−)(e^{+}e^{-}) Pairs in High Energy Nucleus-Nucleus Collisions

We show that the coherent oscillations of the e.m. field induced by the collective quantum fluctuations of the nuclear matter field associated with the giant resonances, with frequencies $\omega_{A}\simeq 78A^{-{1/3}}$ MeV, give rise to a significant $(e^+e^-)$ pair production in high energy Heavy Ion collisions. The approximate parameterless calculation of such yield is in good agreement with recent experimental observations.Comment: 27 pages, 13 figure