The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

Equilibrium Initialization and Stability of Three-Dimensional Gas Disks

We present a new systematic way of setting up galactic gas disks based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disk. We first show that the required circular velocity has no dependence on the height above or below the midplane so long as the gas pressure is a function of density only. The assumption of disks being very thin enables us to decouple the vertical structure from the radial direction. Based on that, the equation of hydrostatic equilibrium together with the reduced Poisson equation leads to two sets of second-order non-linear differential equation, which are easily integrated to set-up a stable disk. We call one approach `density method' and the other one `potential method'. Gas disks in detailed balance are especially suitable for investigating the onset of the gravitational instability. We revisit the question of global, axisymmetric instability using fully three-dimensional disk simulations. The impact of disk thickness on the disk instability and the formation of spontaneously induced spirals is studied systematically with or without the presence of the stellar potential. In our models, the numerical results show that the threshold value for disk instability is shifted from unity to 0.69 for self-gravitating thick disks and to 0.75 for combined stellar and gas thick disks. The simulations also show that self-induced spirals occur in the correct regions and with the right numbers as predicted by the analytic theory.Comment: 17 pages, 10 figures, accepted by MNRA

Prospective randomized trial comparing sutured with sutureless mesh fixation for Lichtenstein hernia repair: long-term results

Background: Following Lichtenstein hernia repair, up to 25% of patients experience prolonged postoperative and chronic pain as well as discomfort in the groin. One of the underlying causes of these complaints are the compression or irritation of nerves by the sutures used to fixate the mesh. We compared the level and rate of chronic pain in patients operated with the classical Lichtenstein technique fixated by sutures to patients with sutureless mesh fixation technique. Methods: A two-armed randomized trial with 264 male patients was performed. After consent, patients were randomized preoperatively. For the fixation of the mesh we used either sutures with slow-absorbing material (PDS 2.0) (group I, n=133) or tissue glue (Histoacryl) (group II, n=131). Follow-up examinations were performed after 3, 12months and after 5years. Results: Patient characteristics in the two groups were similar. No cross-over between groups was observed. After 5years, long-term follow-up could be completed for 59% of subjects. After 5years, 10/85 (11.7%) patients in group I and 3/70 (4.2%) in group II suffered from chronic pain in the groin region (P=0.108). The operation time was significantly shorter in group II (79min vs 73min, P=0.01). One early recurrence occurred in group II (3months). The recurrence rate was 0 and 0% after 12months and 5.9% (5/85) and 10% (7/70) after 5years in group I and group II, respectively (P=0.379). Conclusion: After 5years, the two techniques of mesh fixation resulted in similar rates of chronic pain. Whereas recurrence rates were comparable, fixation of the mesh with tissue glue decreased operating room time significantly. Hence, suture less mesh fixation with Histoacryl is a sensible alternative to suture fixation and should be especially considered for patients prone to pai

Anomalous Fermi Liquid Behavior of Overdoped High-Tc Superconductors

According to a generic temperature vs. carrier-doping (T-p) phase diagram of high-temperature superconductors it has been proposed that as doping increases to the overdoped region they approach gradually a conventional (canonical) Fermi Liquid. However, Hall effect measurements in several systems reported by different authors show a still strong \emph{T}-dependence in overdoped samples. We report here electrical transport measurements of Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-delta} thin films presenting a temperature dependence of the Hall constant, R_H, which does not present a gradual transition towards the T-independent behavior of a canonical Fermi Liquid. Instead, the T-dependence passes by a minimum near optimal doping and then increases again in the overdoped region. We discuss the theoretical predictions from two representative Fermi Liquid models and show that they can not give a satisfactory explanation to our data. We conclude that this region of the phase diagram in YBCO, as in most HTSC, is not a canonical Fermi Liquid, therefore we call it Anomalous Fermi Liquid.Comment: 9 pages, 12 figures, to be published in Phys. Rev.

Pressure Dependence of the Irreversibility Line in Bi2_{2}Sr2_{2}CaCu2_{2}O8+δ_{8+\delta}:Role of Anisotropy in Flux-Line Formation

One of the important problems of high-temperature superconductivity is to understand and ultimately to control fluxoid motion. We present the results of a new technique for measuring the pressure dependence of the transition to superconductivity in a diamond anvil cell. By measuring the third harmonic of the {\it ac} susceptibility, we determine the onset of irreversible flux motion. This enables us to study the effects of pressure on flux motion. The application of pressure changes interplanar spacing, and hence the interplanar coupling, without significantly disturbing the intraplanar superconductivity. Thus we are able to separate the effects of coupling from other properties that might affect the flux motion. Our results directly show the relationship between lattice spacing, effective- mass anisotropy, and the irreversibility line in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$. Our results also demonstrate that an application of 2.5 GPa pressure causes a dramatic increase in interplanar coupling.Comment: 4 pages, 4 figure

Microstructure and pinning properties of hexagonal-disc shaped single crystalline MgB2

We synthesized hexagonal-disc-shaped MgB2 single crystals under high-pressure conditions and analyzed the microstructure and pinning properties. The lattice constants and the Laue pattern of the crystals from X-ray micro-diffraction showed the crystal symmetry of MgB2. A thorough crystallographic mapping within a single crystal showed that the edge and c-axis of hexagonal-disc shape exactly matched the (10-10) and the (0001) directions of the MgB2 phase. Thus, these well-shaped single crystals may be the best candidates for studying the direction dependences of the physical properties. The magnetization curve and the magnetic hysteresis for these single crystals showed the existence of a wide reversible region and weak pinning properties, which supported our single crystals being very clean.Comment: 5 pages, 3 figures. submitted to Phys. Rev.

Tachyon Vacuum Solution in Open String Field Theory with Constant B Field

We show that Schnabl's tachyon vacuum solution is an exact solution of the equation of motion of Witten's open bosonic string field theory in the background of constant antisymmetric two-form field. The action computed at the vacuum solution is given by the Dirac-Born-Infeld factor multiplied to that without the antisymmetric tensor field.Comment: 8 page

Towards a first-principles theory of surface thermodynamics and kinetics

Understanding of the complex behavior of particles at surfaces requires detailed knowledge of both macroscopic and microscopic processes that take place; also certain processes depend critically on temperature and gas pressure. To link these processes we combine state-of-the-art microscopic, and macroscopic phenomenological, theories. We apply our theory to the O/Ru(0001) system and calculate thermal desorption spectra, heat of adsorption, and the surface phase diagram. The agreement with experiment provides validity for our approach which thus identifies the way for a predictive simulation of surface thermodynamics and kinetics.Comment: 4 pages including 3 figures. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions

Two scenarios for the penetration of relativistically intense laser radiation into an overdense plasma, accessible by self-induced transparency, are presented. For supercritical densities less than 1.5 times the critical one, penetration of laser energy occurs by soliton-like structures moving into the plasma. At higher background densities laser light penetrates over a finite length only, that increases with the incident intensity. In this regime plasma-field structures represent alternating electron layers separated by about half a wavelength by depleted regions.Comment: 9 pages, 4 figures, submitted for publication to PR