Maciej Janowicz

Method of multiple scales in quantum optics

Abstract Applications of the method of multiple scales to the quantum-optical problems are reviewed. After a preliminary study of applications to the classical and quantum anharmonic oscillator, several examples in the spontaneous emission, resonance fluorescence, and cavity quantum electrodynamics are analyzed. A preliminary account of application of the method to a model of Bose–Einstein condensates is given. A common thread throughout the main body of the review is the stabilization of the wave function and population of a level due to the phase modulation by an external agent.

Defect Detection in Furniture Elements with the Hough Transform Applied to 3D Data

Defects in furniture elements were detected using data from a commercially available structured light 3D scanner. Out-of-plane deviations down to 0.15 mm were analyzed successfully. The hierarchical, iterated version of the Hough transform was used. The calculation of position of the plane could be separated from that of its direction due to the assumption of nearly horizontal location of the plane, which is natural when the tested elements lie on a horizontal surface.

A Study on Directionality in the Ulam Square with the Use of the Hough Transform

A version of the Hough transform in which the direction of the line is represented by a pair of co-prime numbers has been used to investigate the directional properties of the Ulam spiral. The method reveals the detailed information on the intensities of the lines which can be found in the square and on the numbers of primes contained in these lines. This makes it possible to make quantitative assessments related to the lines. The analysis, among others, confirms the known observation that one of the diagonal directions is more populated with lines than the other one. The results are compared to those made for a square containing randomly located points with a density close to that for the Ulam square of a corresponding size. Besides its randomness, such square also has a directional structure resulting from the square shape of the pixel lattice. This structure does not depend significantly on the size of the square. The analysis reveals that the directional structure of the Ulam square is both quantitatively and qualitatively different from that of a random square. Larger density of lines in the Ulam square along one of the diagonal directions in comparison to the other one is confirmed.

Detection of Surface Defects of Type 'orange skin' in Furniture Elements with Conventional Image Processing Methods

An attempt was made to differentiate between surfaces of furniture elements having the orange skin defect and those free from it. As the detectors, the directional derivative of the image intensity along the dominating light direction and the modulus of the image intensity gradient were used. The detectors were tested on series of images with the small and large light incident angles. In case of both detectors, there existed sufficiently wide ranges of thresholds for which both sensitivity and specificity were

Decoherence of entangled states in two-mode cavities

100\,\%

A four-level “Ξ-system”: Exact solvability and effective evolution operators via multiple scales

for all the 19i¾źimages tested. The ranges of thresholds were wider for the light closer to tangential, and for the detector using the gradient modulus, than for the other cases. The optimum scale of the detectors was found different for each light conditions.

Prediction of Trend Reversals in Stock Market by Classification of Japanese Candlesticks

Pattern recognition analysis based on \(k\)-nearest neighbors classifiers is applied to the representation of the stock market dynamics with the help of the Japanese candlesticks augmented by the accompanying volume of transactions. Examples from a post-emerging Warsaw stock market are given. Conditions under which the Japanese candlesticks appear to have a reasonable predictive power are provided. The dependence of the results on the number of nearest neighbors, the length of the candlestick sequence, and the forecast horizon are shown. Possible ways of the forecast improvement are discussed.

Cellular automaton approach to electromagnetic wave propagation in dispersive media

Decoherence of the Schrodinger-cat states in two-mode cavities are discussed. The cat states are assumed to be produced by the measurement of the energy of a three-level atom which have passed through the cavity. The evolution of the field density matrix is obtained from the Lindblad form of the dissipater at zero temperature. It is shown that the decoherence time of the two-mode cat states critically depends on the degree of entanglement. Implications for decoherence of entanglement in the macroscopic scales are discussed.