Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

Motivated by applications in quantum information and quantum control, a new type of $C$"-numerical range, the relative $C$"-numerical range denoted $W_K(C,A)$, is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical $C$"-numerical range by any of its compact and connected subgroups $K \subset U(N)$. The geometric properties of the relative $C$"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. $W_K(C,A)$ is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical $C$"-numerical range extends to $W_K(C,A)$, as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup $SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2)$, i.e. the $n$-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for $W_{K}(C,A)$ being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for $SU(2) \otimes SU(2)$.Comment: accompanying paper to math-ph/070103

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

Systematics of Fission Barriers in Superheavy Elements

We investigate the systematics of fission barriers in superheavy elements in the range Z = 108-120 and N = 166-182. Results from two self-consistent models for nuclear structure, the relativistic mean-field (RMF) model as well as the non-relativistic Skyrme-Hartree-Fock approach are compared and discussed. We restrict ourselves to axially symmetric shapes, which provides an upper bound on static fission barriers. We benchmark the predictive power of the models examining the barriers and fission isomers of selected heavy actinide nuclei for which data are available. For both actinides and superheavy nuclei, the RMF model systematically predicts lower barriers than most Skyrme interactions. In particular the fission isomers are predicted too low by the RMF, which casts some doubt on recent predictions about superdeformed ground states of some superheavy nuclei. For the superheavy nuclei under investigation, fission barriers drop to small values around Z = 110, N = 180 and increase again for heavier systems. For most of the forces, there is no fission isomer for superheavy nuclei, as superdeformed states are in most cases found to be unstable with respect to octupole distortions.Comment: 17 pages REVTEX, 12 embedded eps figures. corrected abstrac

The hip fracture incidence curve is shifting to the right: A forecast of the age-quake

Background The number of hip fractures has doubled in the last 30–40 years in many countries. Age-adjusted incidence has been reported to be decreasing in Europe and North America, but is there a decreasing trend in all age groups

A multidisciplinary, multifactorial intervention program reduces postoperative falls and injuries after femoral neck fracture

INTRODUCTION: This study evaluates whether a postoperative multidisciplinary, intervention program, including systematic assessment and treatment of fall risk factors, active prevention, detection, and treatment of postoperative complications, could reduce inpatient falls and fall-related injuries after a femoral neck fracture. METHODS: A randomized, controlled trial at the orthopedic and geriatric departments at Umeå University Hospital, Sweden, included 199 patients with femoral neck fracture, aged  ≥70 years. RESULTS: Twelve patients fell 18 times in the intervention group compared with 26 patients suffering 60 falls in the control group. Only one patient with dementia fell in the intervention group compared with 11 in the control group. The crude postoperative fall incidence rate was 6.29/1,000 days in the intervention group vs 16.28/1,000 days in the control group. The incidence rate ratio was 0.38 [95% confidence interval (CI): 0.20 – 0.76, p = 0.006] for the total sample and 0.07 (95% CI: 0.01–0.57, p=0.013) among patients with dementia. There were no new fractures in the intervention group but four in the control group. CONCLUSION: A team applying comprehensive geriatric assessment and rehabilitation, including prevention, detection, and treatment of fall risk factors, can successfully prevent inpatient falls and injuries, even in patients with dementia

Multiple Interactions and the Structure of Beam Remnants

Recent experimental data have established some of the basic features of multiple interactions in hadron-hadron collisions. The emphasis is therefore now shifting, to one of exploring more detailed aspects. Starting from a brief review of the current situation, a next-generation model is developed, wherein a detailed account is given of correlated flavour, colour, longitudinal and transverse momentum distributions, encompassing both the partons initiating perturbative interactions and the partons left in the beam remnants. Some of the main features are illustrated for the Tevatron and the LHC.Comment: 69pp, 33 figure

Forward Neutron Production at the Fermilab Main Injector

We have measured cross sections for forward neutron production from a variety of targets using proton beams from the Fermilab Main Injector. Measurements were performed for proton beam momenta of 58 GeV/c, 84 GeV/c, and 120 GeV/c. The cross section dependence on the atomic weight (A) of the targets was found to vary as $A^(alpha)$ where $\alpha$ is $0.46\pm0.06$ for a beam momentum of 58 GeV/c and 0.54$\pm$0.05 for 120 GeV/c. The cross sections show reasonable agreement with FLUKA and DPMJET Monte Carlos. Comparisons have also been made with the LAQGSM Monte Carlo.Comment: Accepted for publication in Physical Review D. This version incorporates small changes suggested by referee and small corrections in the neutron production cross sections predicted by FLUK

Measurement of Charged Pion Production Yields off the NuMI Target

The fixed-target MIPP experiment, Fermilab E907, was designed to measure the production of hadrons from the collisions of hadrons of momenta ranging from 5 to 120 GeV/c on a variety of nuclei. These data will generally improve the simulation of particle detectors and predictions of particle beam fluxes at accelerators. The spectrometer momentum resolution is between 3 and 4%, and particle identification is performed for particles ranging between 0.3 and 80 GeV/c using $dE/dx$, time-of-flight and Cherenkov radiation measurements. MIPP collected $1.42 \times10^6$ events of 120 GeV Main Injector protons striking a target used in the NuMI facility at Fermilab. The data have been analyzed and we present here charged pion yields per proton-on-target determined in bins of longitudinal and transverse momentum between 0.5 and 80 GeV/c, with combined statistical and systematic relative uncertainties between 5 and 10%.Comment: 15 pages, 13 figure

Solution of the Kwiecinski evolution equations for unintegrated parton distributions using the Mellin transform

The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general case, as well as in a small-b expansion which converges fast for b Lambda_QCD sufficiently small. We also discuss the asymptotic limit of large bQ and show that the distributions generated by the evolution decrease with b according to a power law. Numerical results are presented for the pion distributions with a simple valence-like initial condition at the low scale, following from chiral large-N_c quark models. We use two models: the Spectral Quark Model and the Nambu--Jona-Lasinio model. Formal aspects of the equations, such as the analytic form of the b-dependent anomalous dimensions, their analytic structure, as well as the limits of unintegrated parton densities at x -> 0, x -> 1, and at large b, are discussed in detail. The effect of spreading of the transverse momentum with the increasing scale is confirmed, with growing asymptotically as Q^2 alpha(Q^2). Approximate formulas for for each parton species is given, which may be used in practical applications.Comment: 18 pages, 6 figures, RevTe

Measurement of beauty production in deep inelastic scattering at HERA

The beauty production cross section for deep inelastic scattering events with at least one hard jet in the Breit frame together with a muon has been measured, for photon virtualities Q^2 > 2 GeV^2, with the ZEUS detector at HERA using integrated luminosity of 72 pb^-1. The total visible cross section is sigma_b-bbar (ep -> e jet mu X) = 40.9 +- 5.7 (stat.) +6.0 -4.4 (syst.) pb. The next-to-leading order QCD prediction lies about 2.5 standard deviations below the data. The differential cross sections are in general consistent with the NLO QCD predictions; however at low values of Q^2, Bjorken x, and muon transverse momentum, and high values of jet transverse energy and muon pseudorapidity, the prediction is about two standard deviations below the data.Comment: 18 pages, 4 figure