The Clifford-Fourier Transform {mathcal {F}_o} and Monogenic Extensions

In the last decade several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus, and a connection between the Fourier transform and this new transform. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.     

A highly sensitive and selective method for the extraction-spectrophotometric determination of cobalt

The method is based on the highly sensitive reaction between cobalt and 4-(5-bromo-2-pyridylazo)-l,3-diaminobenzene. The cationic complex in slightly acidic solution is quantitatively extracted into chloroform as an ion pair with anthraquinone sulfonate; interfering ions are retained in the aqueous phase by selected masking agents. The cobalt complex is then rapidly back-extracted into 2.4 M HCl and measured at 573 nm (? = 1.16 × 10⁵ l mol^-1 cm^-1).     

Equirépartition des coefficients de Fourier des fonctions L de carrés et de cubes symétriques

Dans ce travail, on étudie l’équirépartition et l’équirépartition harmonique des coefficients de Fourier des fonctions L de carrés et de cubes symétriques d’une forme primitive.     

Broadband gain-clamped linear quantum dash optical amplifiers

The linear optical gain of gain-clamped quantum dash semiconductor optical amplifiers (GCSOAs) has been investigated using the rate equation model. The gain spectrum of GCSOA for different wavelength detuning and different doping has been studied. Our analysis shows that the linear gain can be increased as the laser wavelength is detuned to high wavelength where the peak of the optical gain, which is found at wavelengths below the ground state wavelength, is shifted to lower wavelength as the laser wavelength is increased. We find that doping the dashes by either N-type or P-type enhances the linear optical gain and shifts the gain peak to lower wavelength. Moreover, we found that GCSOA with lightly N-type doping demonstrates large separation between the laser and the amplifier wavelength. Also we find that small inhomogeneous line broadening enhances the linear gain peak, shifts the gain peak to wavelength lower than the GS wavelength and widens the gain spectrum.     

Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J _z is different from the lateral one J _l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J _l ? J _z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.     

Effect of static disorder in an electron Fabry-Perot interferometer with two quantum scattering centers

In a recent paper—F. Ciccarello et al., New J. Phys. 8, 214 (2006)—we have demonstrated that the electron transmission properties of a one-dimensional (1D) wire with two identical embedded spin-1/2 impurities can be significantly affected by entanglement between the spins of the scattering centers. Such an effect is of particular interest in the control of the transmission of quantum information in nanostructures and can be used as a detection scheme of maximally entangled states of two localized spins. In this letter, we relax the constraint that the two magnetic impurities are equal and investigate how the main results presented in the above paper are affected by a static disorder in the exchange coupling constants of the impurities. Good robustness against deviation from impurity symmetry is found for both the entanglement dependent transmission and the maximally entangled states generation scheme.