We present a phase-shifting holography method in k space that allows us to investigate the phase and amplitude of optical Bloch waves. The method is based on a Fourier space imaging technique combined with a Mach-Zehnder interferometer. Using a W3 photonic crystal waveguide as a model system, we determine, with high accuracy, both the intensity and the phase of the envelope function of the Bloc...

To enhance the performance of quantum-behaved PSO, some improvements are proposed. First, an encoding method based on the Bloch sphere is presented. In this method, each particle carries three groups of Bloch coordinates of qubits, and these coordinates are actually the approximate solutions. The particles are updated by rotating qubits about an axis on the Bloch sphere, which can simultaneousl...

The Wigner-Kirkwood h-expansion of theWigner transform of the Bloch density can be resummed in the case of non local potentials if we keep only up to second order derivatives of the Wigner transform of the non-local potential with respect to the phase space variables. We also investigate a second approximation to the Bloch density where care has been taken with respect to a consistent h expansi...

The boundedness and compactness of the integral-type operator Luðf ÞðzÞ 1⁄4 Z 1 0 Rf ðuðtzÞÞgðtzÞ dt t ; z 2 B; where g is a holomorphic function on the open unit ball B in C such that g(0) = 0 and u is a holomorphic self-map of B, from Bloch-type spaces Bl and Bl;0, where l is a normal weight, to F(p,q,s) space on B are characterized, solving a recent open problem. 2011 Elsevier Inc. All right...