Generation of NOON States in Waveguide Arrays

A method to generate NOON states with three photons by injecting photons in an array of three waveguides is presented. Conditional measurements project the wave function in a given (desired) state. In passing, it is shown how the array of three waveguides, that effectively reproduces the interaction of three fields, may be reduced to the interaction of two fields.     

Time‐resolved in situ tomography for the analysis of evolving metal‐foam granulates

An experimental setup has been developed that allows for capturing up to 25 tomograms s^?1 using the white X‐ray beam at the experimental station EDDI of BESSY II, Berlin, Germany. The key points are the use of a newly developed, precise and fast rotation stage, a very efficient scintillator and a fast CMOS camera. As a first application, the foaming of aluminium alloy granules at 923 K was investigated in situ. Formation and growth of bubbles in the liquid material were observed and found to be influenced by the limited thermal conductivity in the bulk granules. Changes that took place between two tomographic frames separated in time by 39 ms could be detected and analysed quantitatively.     

Orthogonal polynomials on the unit circle and their derivatives

We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle.     

A smoothing method for mathematical programs with equilibrium constraints

Received May 3, 1996 / Revised version received November 19, 1997 Published online January 20, 1999     

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.     

Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.