Representations of O(N) Spin Models by Self-Avoiding Random Walks

We establish that correlation functions of classical lattice spin models can be represented by series expansions in terms of self-avoiding random walks. Using this, we get new upper bounds of critical temperatures of the O(N) symmetric classical Heisenberg models. Received: 21 March 1996 / Accepted: 26 July 1996     

Fabrication of BDD quantum node switches on embedded GaAs quantum wires grown by selective MBE

In view of applications to hexagonal binary decision diagram (BDD) LSIs, a first attempt is made to form quantum BDD node switches on selectively grown (SG) embedded quantum wires (QWRs) by molecular beam epitaxy (MBE). SG branch switches controlled by a Schottky wrap gate (WPG) were successfully fabricated by MBE growth and subsequent device processing. Gate control characteristics were studied by gate-dependent Shubnikov–de-Haas measurements, and the behavior was found to be similar to that of devices fabricated on wires by etching. The switch exhibited clear conductance quantization at low temperature, and temperature dependence of the voltage slope of conductance jump was clarified. A Y-branch BDD node device using two SG branch switches was successfully fabricated, and realized clear path switching characteristics.     

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.