Ultrashort-pulse fiber ring lasers

Received: 18 February 1997/Revised version: 22 April 1997     

Semiclassical Analysis for Magnetic Scattering by Two Solenoidal Fields: Total Cross Sections

The fact that vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the Aharonov–Bohm effect (A–B effect). We study this quantum effect through the semiclassical analysis on total cross sections in the magnetic scattering by two solenoidal (point-like) fields with total flux vanishing in two dimensions. We derive the asymptotic formula with first three terms. The system with two parallel fields seems to be important in practical aspects as well as in theoretical aspects, because it may be thought of a toroidal solenoid with zero cross section in three dimensions under the idealization that the two fields connect at infinity in their direction. The corresponding classical mechanical system has the trajectory oscillating between two centers of fields. The special emphasis is placed on analyzing how the trapping effect from classical mechanics is related to the A–B quantum effect in the semiclassical asymptotic formula. Submitted: September 3, 2006. Accepted: January 10, 2007.     

Scattering of a plane wave from a periodic random surface: a probabilistic approach

This paper deals with a probabilistic formulation of the wave scattering from a periodic random surface. When a plane wave is incident on a random surface described by a periodic stationary stochastic process, it is shown by a group-theoretic consideration that the scattered wave may have a stochastic Floquet form, i.e. a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then written by a harmonic series representation similar to a Fourier series, where Fourier coefficients are mutually correlated stationary processes instead of constants. The mutually correlated stationary processes are represented by Wiener - Hermite functional series with unknown coefficient functions called Wiener kernels. In case of a slightly rough surface and TE wave incidence, low-order Wiener kernels are determined from the boundary condition. Several statistical properties of the scattering are calculated and illustrated in figures.     

Testing EPR locality using B-mesons

We study the possibility of testing local realistic theory (LRT) based on the Bell inequality for the correlations in the decay modes of entangled K or B-mesons. It is shown that such a test is possible for a restricted class of LRT, despite the passive nature of decay events and/or the non-unitary treatment of the correlations which invalidate the test for general LRT. Unfortunately, the present setup of the KEKB (Belle) experiment, where the coherence of entangled B-mesons has been confirmed recently, does not admit such a test due to the indeterminacy in the separate decay times of the entangled pairs.     

The chemistry of O-silylated ketene acetals; diastereoselective Aldol reaction of 2,3-O-isopropylidene-D (and L)-glyceraldehydes leading to 2-deoxy-D (and L)-riboses

Diastereoselective carbon-carbon bond forming reaction of 2,3-O-isopropylidene-D (and L)-glyceraldehydes (D and L-2) with ketene silyl acetals (1a,b) occurred in acetonitrile under mild conditions to give the corresponding $\text{anti}$-β-siloxyesters (D and L-3a) as major products, which could be converted through a few additional steps to 2-deoxy-D(and L)-riboses.