Selective correlations in finite quantum systems and the Desargues property
The Desargues property is well known in the context of projective geometry. An analogous property is presented in the context of both classical and Quantum Physics. In a classical context, the Desargues property implies that two logical circuits with the same input, show in their outputs selective correlations. In general their outputs are uncorrelated, but if the output of one has a particular value, then the output of the other has another particular value. In a quantum context, the Desargues property implies that two experiments each of which involves two successive projective measurements, have selective correlations. For a particular set of projectors, if in one experiment the second measurement does not change the output of the first measurement, then the same is true in the other experiment.
The generation and behavior of the fractal Koch array factor from a Kaiser window generator is studied. The main advantage of using Kaiser windows is that pattern parameters become much more flexible through altering the Kaiser window. The mainlobe width, current distribution, side-lobe ratio are now adjustable. Different reduced array structures can be obtained by using different threshold levels. Higher threshold values result in a highly reduced number of elements but they may highly distort the pattern and, hence, the multiband behavior. Finally, we study the effect of quantization of the feeding values. Quantization is necessary for implementation and simplification purposes. Several configurations of current distributions with the corresponding patterns are illustrated for different quantization levels. It is shown that moderate quantization keeps the same interesting similarity properties at several bands.