Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

Designing strategy to enhance mode selectivity of higher-output oxide-confined vertical-cavity surface-emitting lasers

Performance of modern oxide-confined (OC) vertical-cavity surface-emitting diode lasers (VCSEL s) is more sensitive to the construction details than in the case of other VCSEL s. In particular, a stable single-fundamental-mode operation is difficult to be achieved in these VCSEL s especially in higher-output large-size continuous-wave (cw) operating devices at higher temperatures. In the present paper, an operation of OC VCSEL s has been investigated with the aid of the comprehensive fully self-consistent model using the (GaIn)(NAs)/GaAs quantum-well VCSEL with two oxide apertures as a typical example. A new approach is proposed to enhance cw RT single-fundamental-mode low-threshold operation in higher-output OC VCSEL s. One of their oxide apertures should be shifted to the node position of the resonator standing wave where it is working as the electrical aperture only. Then diameters of both apertures may be changed independently giving an additional degree of freedom for VCSEL designing, which enables their optimisation. While the larger-diameter optical aperture placed in the anti-node position creates an efficient radial waveguiding effect, the smaller-diameter electrical aperture enhances a more uniform current injection into the VCSEL active region. Due to combining influence of both the apertures, the single-fundamental-mode operation is predicted in a large device with the 10-m-diameter active region even for 80 K active-region temperature increase over RT of the ambient. An impact of intentional detuning at room-temperature (RT) of VCSEL active-region gain spectrum towards shorter wavelengths with respect to the resonator mode improves mode selectivity is also analysed. PACS  42.55.Px; 02.60.Cb; 85.60.Bt     

High-numerical-aperture microlens shape measurement with digital holographic microscopy

In this Letter, we introduce an algorithm that overcomes limitations in shape measurement by holographic microscopic methods in cases of micro-optical elements with high NA, such as microlenses. The presented algorithm provides a simple method for shape reconstruction from interferometrically measured phase. The algorithm is based on the analysis of local ray transition through the measured object. We develop algorithms for holographic configurations working in transmission and reflection. The accuracy of the developed algorithms is proved by experiments and extensive simulations. We present an experiment in a holographic Mach-Zehnder configuration where we have measured and successfully reconstructed the height distribution of spherical and cylindrical microlenses with NA up to 0.3.     

Characterization of CaTi0.9Fe0.1O3/La0.98Mg0.02NbO4 composite

A composite of CaTi_0.9Fe_0.1O₃ and electrolyte material, i.e. magnesium doped La_0.98Mg_0.02NbO₄ was prepared and studied. The phase content and the sample microstructure was examined by an X-ray diffraction method and scanning electron microscopy. EDS measurements were done both for composite samples and the diffusion couple. The electrical properties were studied by four terminal DC method. The high-temperature interaction between the two components of the composite has been observed. It has been suggested that lanthanum diffused into the perovskite phase and substituted for calcium whereas calcium and niobium formed the Ca₂Nb₂O₇ pyrochlore phase. At 1500°C very large crystallites of the pyrochlore were observed. Regardless of strong interaction between the composite components, its total conductivity was weakly dependent on the sintering temperature.     

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Ho?ava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.     

Theoretical study of the influence of laser-induced defects on the adsorption of gases on solid surfaces

Laser treatment of a solid surface was modeled by applying an analytical theory as well as by using Monte Carlo simulations. The crystalline surface was assumed to be initially smooth and chemically uniform, that is free of impurities built into the structure. Creation of surface defects by a laser beam was assumed to have entirely random nature. In particular, the surface was assumed to have been scanned by the beam focused successively on randomly chosen points. In the course of the ablation process, the beam produces a pyramidal crater whose dimensions are proportional to the applied laser power. According to the assumed nature of the scanning procedure, the craters formed by the beam are allowed to overlap. The influence of the number of laser pulses and the crater dimensions on the structural and adsorptive properties of the surface were examined by analysis of the variation of the mean surface depth and the surface width. Changes in the adsorptive properties were also estimated by the calculation of the thermally programmed desorption (TPD) spectra of monomolecular adsorbates desorbed from laser-treated surfaces. Additionally, equilibrium adsorption isotherms were calculated for the obtained surfaces.     

3D MR imaging of dental cavities-an in vitro study

A 3D spin-echo (3D SE) pulse sequence was used on a 4.7 T research MRI system to produce images of extracted human first molar tooth placed in CuSO4 water solution. The maximal resolution achieved was 35 x 63 x 300 microm3 in read and two phase directions, respectively. The high-intensity signal from water in solution together with the lack of signal from mineralized tooth tissue produce very good contrast allowing to visualize topography of outer and inner surfaces of the tooth. The 3D MR data were median filtered, binarized and then divided into separate segments corresponding to the inner tooth cavities and the hard tooth tissue. The topography of the root canals was visualized and the canals volume was calculated. The presented technique may be used for quantitative analysis of the root canal cavities shape and volume. The results of such an analysis may be applied for estimation of the quality of the impressional mapping methods in restorative dentistry or as an alternative non-impressional 3D mapping method.