Quantum effects of periodic orbits for the kicked top

We analyze traces of powers of the time evolution operator of a periodically kicked top. Semiclassically, such traces are related to periodic orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovered via a Fourier transform. A breakdown of the stationary phase approximation is detected. The quasi energy spectrum remains elusive due to lack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coefficients of the characteristic polynominal of the Floquet operator. Statistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.     

A unified conformal model for fundamental interactions without dynamical Higgs field

A Higgsless model for strong, electroweak and gravitational interactions is proposed. This model is based on the local symmetry group SU(3)×SU(2)_L×U(1)×C,where C is the local conformal symmetry group. The natural minimal conformally invariant form of total Lagrangian is postulated. It contains all standard model fields and gravitational interaction. Using the unitary gauge and the conformal scale fixing conditions, we can eliminate all four real components of the Higgs doublet in this model. However, the masses of vector mesons, leptons, and quarks are automatically generated and are given by the same formulas as in the conventional standard model. In this manner one gets the mass generation without the mechanism of spontaneous symmetry breaking and without the remaining real dynamical Higgs field. The gravitational sector is analyzed, and it is shown that the model admits in the classical limit the Einsteinian form of gravitational interactions.     

Polychromatic light interferometer for high-accuracy positioning

Superposition of different-wavelength, multimode- and single-mode laser diode beams is investigated to locate the fringe of zero interference order in a Twyman-Green interferometer. The possibility of central fringe detection using three multimode laser diodes or one single-mode together with a pair of multimode laser diodes is shown. If a single-mode laser diode is applied, a simultaneous fringe-counting technique for displacement measurement is available. The influence of the angle between wavefronts entering the interferometer is analyzed. A repeatability of about 5 nm is shown for surface position determination when using three-beam source.     

Optical Space of the Reissner-Nordström Solutions

We present an exhaustive discussion of the embedding diagrams for the optical geometry of the Reissner-Nordström solutions. Whereas in the black hole sector there are no qualitative differences with respect to the Schwarzschild case, the diagrams are considerably different if naked singularities are present. Our treatment is sufficiently general that it can be applied also to any other static spherically symmetric spacetime.     

Different faces of chaos in FRW models with scalar fields—geometrical point of view

FRW cosmologies with conformally coupled scalar fields are investigated in a geometrical way by the means of geodesics of the Jacobi metric. In this model of dynamics, trajectories in the configuration space are represented by geodesics. Because of the singular nature of the Jacobi metric on the boundary set of the domain of admissible motion, the geodesics change the cone sectors several times (or an infinite number of times) in the neighborhood of the singular set .

We show that this singular set contains interesting information about the dynamical complexity of the model. Firstly, this set can be used as a Poincaré surface for construction of Poincaré sections, and the trajectories then have the recurrence property. We also investigate the distribution of the intersection points. Secondly, the full classification of periodic orbits in the configuration space is performed and existence of UPO is demonstrated. Our general conclusion is that, although the presented model leads to several complications, like divergence of curvature invariants as a measure of sensitive dependence on initial conditions, some global results can be obtained and some additional physical insight is gained from using the conformal Jacobi metric. We also study the complex behavior of trajectories in terms of symbolic dynamics.     

On a class of free Lévy laws related to a regression problem

The free Meixner laws arise as the distributions of orthogonal polynomials with constant-coefficient recursions. We show that these are the laws of the free pairs of random variables which have linear regressions and quadratic conditional variances when conditioned with respect to their sum. We apply this result to describe free Lévy processes with quadratic conditional variances, and to prove a converse implication related to asymptotic freeness of random Wishart matrices.     

Top ten accelerating cosmological models

Recent astronomical observations indicate that the Universe is presently almost flat and undergoing a period of accelerated expansion. Basing on Einstein's general relativity all these observations can be explained by the hypothesis of a dark energy component in addition to cold dark matter (CDM). Because the nature of this dark energy is unknown, it was proposed some alternative scenario to explain the current accelerating Universe. The key point of this scenario is to modify the standard FRW equation instead of mysterious dark energy component. The standard approach to constrain model parameters, based on the likelihood method, gives a best-fit model and confidence ranges for those parameters. We always arbitrary choose the set of parameters which define a model which we compare with observational data. Because in the generic case, the introducing of new parameters improves a fit to the data set, there appears the problem of elimination of model parameters which can play an insufficient role. The Bayesian information criteria of model selection (BIC) is dedicated to promotion a set of parameters which should be incorporated to the model. We divide class of all accelerating cosmological models into two groups according to the two types of explanation acceleration of the Universe. Then the Bayesian framework of model selection is used to determine the set of parameters which gives preferred fit to the SNIa data. We find a few of flat cosmological models which can be recommend by the Bayes factor. We show that models with dark energy as a new fluid are favoured over models featuring a modified FRW equation.     

A novel liquid crystal light modulator

We present a conception of two optical modulators. One of these, which we have called the scattering liquid crystal cell seems to be promising with a view to possible applications. We assumed that the modulator could be used in optical logic as a gate element, but other applications in optoelectronics would appear also to be possible. Some preliminary results of an experimental examination of the modulators are also presented.