Phase control in a coherent superposition of degenerate quantum states through frequency control

We demonstrate a controlled phase change of π in a degenerate superposition by altering a laser frequency by only 10 MHz. The method relies on the preparation of an adiabatic state involving the M = ±2 and M = 0 states of the ³P₂ (J = 2) level of metastable neon. Dependent on the frequency, the preparation proceeds either by stimulated Raman adiabatic passage (STIRAP) or by coherent population trapping (CPT). In the former case the superposition is prepared by adiabatic transfer induced in an extended tripod linkage scheme. In the latter case population is optically pumped into the Zeeman manifold of the level ³P₂. The population which does not reach a dark state decays to the ground state of neon. The amplitudes and relative phases of the dark states differ for the two cases. The phase change is monitored using the method of phase-to-population mapping.     

Operator orderings and functional formulations of quantum and stochastic dynamics

We study the connection between operator ordering schemes and thec-number formulations of quantum mechanics, which are based on generating functionals and functional integrals. We show by explicit construction that different operator ordering schemes are related to different functional and functional integral formulations of quantum mechanics. The results of these considerations are applied to classical non-linear stochastic dynamics by using the formal analogy between the Fokker-Planck equation and the Schrödinger equation.     

A mixed finite element method for solving the nonstationary stokes equation

Summary This paper deals with a mixed finite element method for approximating a fourth order initial value problem arising from the nonstationary Stokes problem. For piecewise linear shape functions error estimates are given with convergence rates similar to the elliptic case. Some numerical computations will illustrate the theoretical results.     

Monoid Valuations and Value Ordered Supervaluations

We complement two papers on supertropical valuation theory ([11 Izhakian , Z. , Knebusch , M. , Rowen , L. ( 2011 ). Supertropical semirings and supervaluations . J. Pure and Applied Alg. 215 ( 10 ): 2431 – 2463 . Preprint at arXiv:1003.1101 .[Crossref], [Web of Science ®] , [Google Scholar]], [12 Izhakian , Z. , Knebusch , M. , Rowen , L. ( 2013 ). Dominance and transmissions in supertropical valuation theory . Commun. Algebra 41 ( 7 ): 2736 – 2782 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]) by providing natural examples of m-valuations (= monoid valuations), and afterwards of supervaluations and transmissions between them. These supervaluations have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. We develop the basics of the theory of such semirings and transmissions.     

Resonance splitting in gyrotropic ring resonators

We present the theoretical concept of an optical isolator based on resonance splitting in a silicon ring resonator covered with a magneto-optical polymer cladding. For this task, a perturbation method is derived for the modes in the cylindrical coordinate system. A polymer magneto-optical cladding causing a 0.01 amplitude of the off-diagonal element of the dielectric tensor is assumed. It is shown that the derived resonance splitting of the clockwise and counterclockwise modes increases for smaller ring radii. For the ring with a radius of approximately 1.5μm, a 29GHz splitting is demonstrated. An integrated optical isolator with a 10μm geometrical footprint is proposed based on a critically coupled ring resonator.     

Energy Dispersive X-Ray Fluorescence Analysis and X-Ray Microanalysis of Medieval Silver Coins

 Austrian medieval silver/copper coins were investigated at their surfaces by energy dispersive X-ray fluorescence analysis (EDXRF) and at the cross-sections by X-ray microanalysis in the scanning electron microscope (SEM/EDX) in order to estimate the error occurring when corroded objects of art and archaeology are analyzed on the surface by non-destructive methods. Additionally, Ag/Cu-standards were treated in diluted sulphuric acid and the depletion of copper on the surface was measured by EDXRF. By calculating the ratio of the Ag-K/Ag-L intensity the process of blanching could be studied.     

(NH4)4Na2[V10O28]·10H2O

Tetra­ammonium disodium decavanadate decahydrate crystallizes in the triclinic system in space group P. The structure contains typical centrosymmetric OV₆ double octahedra and centrosymmetric pairs of edge‐shared NaO₆ double octahedra forming a layered structure. In contrast to other monovalent cationic decavanadates, the NaO₆ double octahedra are integrated in the layer.