Uniform approximation: The non-locally convex case

IfS is a compact Hausdorff space of finite covering dimension and (E, τ) is a real or complex topological vector space (not necessarily locally convex), we prove a Weierstrass-Stone theorem for subsets ofC(S;E), the space of all continuous functions fromS intoE, equipped with the topology of uniform convergence overS.     

Homoclinic phenomena in the gravitational collapse

A class of Bianchi IX cosmological models is shown to have chaotic gravitational collapse, due to Poincaré's homoclinic phenomena. We can program such models so that for any given positive integer N (N=∞ included) the universe undergoes N non-periodic oscillations (each oscillation requiring a long time) before collapsing. For N=∞ the universe undergoes periodic oscillations.     

Flavour violation in supersymmetric theories

We investigate in detail the question of lepton-flavour violation in a SU(2) × U(1) supersymmetric model, where the breaking of supersymmetry (SUSY) is achieved through the coupling to N = 1 supergravity. It is shown that in the limit of degenerate neutrino masses, lepton flavour is exactly conserved. Allowing for neutrino masses compatible with present experimental limits, we analyse SUSY contributions to several lepton-flavour violating processes, comparing the size of these contributions with those already present in the standard Glashow-Salam-Weinberg model. In the case of μ → eγ, SUSY leads to a branching ratio two or three orders of magnitude larger than the corresponding branching ratio in the standard model, for gravitino and photino masses compatible with the experimental limits on the muon anomalous magnetic moment. In contrast, SUSY contributions to are always small, of the order of 10⁻² of the corresponding amplitudes in the standard model, if the gravitino and photino masses are constrained by the K_L − K_S mass difference.     

Does QCD have infrared renormalons?

We give a naïve perturbative proof of the existence of infrared renormalons for large distance asymptotically free theories. We argue that the extension of the result for small distance asymptotically free theories is not obvious. Indeed we do not find infrared renormalons for QCD.     

Quantum entanglement via superradiance of a Bose-Einstein condensate

We adopt the coherence and built-in swap mechanism in sequential superradiance as a tool for obtaining continuous-variable (electric/magnetic fields) quantum entanglement of two counter-propagating pulses emitted from the two end-fire modes. In the first-sequence, end-fire modes are entangled with the side modes. In the second sequence, this entanglement is swapped to in between the two opposite end-fire modes. Additionally, we also examine the photon number correlations. No quantum correlations is observed in this variable.     

Time-resolved imaging of fluorescent inclusions in optically turbid medium — phantom study

We present results of application of a time-resolved optical system for imaging of fluorescence excited in an inclusion containing indocyanine green (ICG), and located in optically turbid medium. The developed imaging system enabled simultaneous acquisition of fluorescence and diffusive reflectance. Eight independent time-resolved measurement channels based on time-correlated single photon counting technique were applied. In four of these channels, used for the fluorescence detection, sets of filters were applied in order to block the excitation light. Fast optomechanical switches allowed us to illuminate sequentially nine different spots on the surface of the studied object and finally 4×4 pixels maps at excitation and emission wavelengths were obtained. A liquid phantom used in this study consists of the fish tank filed with a solution ofmilk and water with black ink added to obtain optical properties in the range of the optical properties typical for the living tissue. A gel ball of a diameter of 5 mm with precisely controlled concentration of ICG was immersed in the liquid. The measurements were performed for inclusion located at different depths and for various ICG concentrations in the gel ball and in the surrounding liquid. The recorded distributions of times of arrival (DTA) of fluorescence photons and times of flight (DTOF) of diffusely reflected photons were analyzed by calculation of their statistical moments. We observed specific changes in moments of the measured DTAs as a function of depth of immersion of the fluorescent inclusion in the medium. We noted also that the changes of moments depend significantly on concentration of the dye in the fluorescence inclusion as well as in the surrounding liquid.     

Advantages of fluorescence over diffuse reflectance measurements tested in phantom experiments with dynamic inflow of ICG

Time-resolved measurements of diffuse reflectance and fluorescence were carried out using phantom with dynamic inflow of indocyanine green (ICG) in tubes located at different depths. Better sensitivity of fluorescence signals related to the inflow of the dye was observed in comparison to simultaneously acquired diffuse reflectance. Obtained results can be referred to results of in-vivo measurements. We have observed much larger amplitude of changes in relative number of detected photons, mean time of flight and variance of the distributions of times of arrival of fluorescence photons than amplitudes of respective parameters measured from diffuse reflectance distributions of times of flight of photons. The constructed phantom allows us to study influence of concentration of the dye in the tube and the surrounding medium as well as temporal relation between appearance of the boli in deeper and superficial tube. Results of the study were used in optimization of the time-resolved multichannel system for simultaneous monitoring of fluorescence and reflectance.     

A two-Higgs doublet model with remarkable CP properties

We analyze generalized CP symmetries of two-Higgs doublet models, extending them from the scalar to the fermion sector of the theory. We show that, other than the usual CP transformation, there is only one of those symmetries which does not imply massless charged fermions. That single model which accommodates a fermionic mass spectrum compatible with experimental data possesses a remarkable feature. Through a soft breaking of the symmetry it displays a new type of spontaneous CP violation, which does not occur in the scalar sector responsible for the symmetry breaking mechanism but, rather, in the fermion sector.     

Multipartite entangled states with two bosonic modes and qubits

We theoretically investigate the role of different phases of coupling constants in the dynamics of atoms and two cavity modes, observing deterministic generation of prototype or hybrid Bell, W, GHZ, and cluster states. Commonly induced dipole-dipole interactions (far-off resonance) are inhibited between particular pairs of qubits under suitable choice of those phases. We evaluate the generation fidelities when imperfections such as dissipative environments and time precision errors are considered. We show violation of local realism for the generated cluster state under such imperfections, even when approaching the weak coupling regime.