We begin with a prior observation by one of us that Thomas precession in the nonrelativistic limit of the Dirac equation may be attributed to a nonabelian Berry vector potential. We ask what object produces the nonabelian potential in parameter space, in the same sense that the abelian vector potential arising in the adiabatic transport of a nondegenerate level is produced by a monopole, (cente...

In a nondegenerate system, the abelian Berry’s phase will never cause transitions among the Hamiltonian’s eigenstate. However, in a degenerate system, it is well known that the state transition can be caused by the non-abelian Berry phase. Actually, in a such a system, the phase factor is not always nonabelian. Even in the case that the phase is a nondiagonal matrix, it still can be an abelian ...

We present a source of correlated photon pairs that relies on spontaneous parametric scattering in microstructure fiber. Quantum correlations are shown between photon pairs that are generated through four-photon scattering where the pump photons are degenerate at a wavelength of 749 nm and the signal and idler photons are nondegenerate at wavelengths of 761 nm and 737 nm, respectively. Careful ...

We prove well-posedness (existence and uniqueness) results for a class of degenerate reaction-diffusion systems. A prototype system belonging to this class is provided by the bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The existence result, which constitutes the main thrust of this paper, is proved by means of a nondegenerate appr...

Although the general linear complementarity problem (LCP) is NP-complete, there are special classes that can be solved in polynomial time. One example is the type where the defining matrix is nondegenerate and for which the n-step property holds. In this paper we consider an extension of the property to the degenerate case by introducing the concept of an extended n-step vector and matrix. It i...

We discuss application of population synthesis for binary stars to progenitors of SN Ia. We show that the only candidate systems able to support the rate of SNe Ia νIa ∼ 10 −3 yr both in old and young populations are merging white dwarfs. In young populations (∼ 1 Gyr) edge-lit detonations in semidetached systems with nondegenerate helium star donors are also able to support a similar νIa. The ...

This article is dedicated to the centenary of the local CR equivalence problem, formulated by Henri Poincaré in 1907. The first part gives an account of Poincaré’s heuristic counting arguments, suggesting existence of infinitely many local CR invariants. Then we sketch the beautiful completion of Poincaré’s approach to the problem in the work of Chern and Moser on Levi nondegenerate hypersurfac...

We show that the degeneracy parameter of a trapped Bose gas can be changed adiabatically in a reversible way, both in the Boltzmann regime and in the degenerate Bose regime. We have performed measurements on spin-polarized atomic hydrogen in the Boltzmann regime, demonstrating reversible changes of the degeneracy parameter (phase-space density) by more than a factor of 2. This result is in good...

The origin of ferromagnetism in semimagnetic III-V materials is discussed. The indirect exchange interaction caused by virtual electron excitations from magnetic impurity acceptor levels to the valence band can explain ferromagnetism in GaAs(Mn) in both degenerate and nondegenerate samples. Formation of ferromagnetic clusters and the percolation picture of phase transition describes well all av...

A recent progress on the complete enumeration of oriented matroids enables us to generate all combinatorial types of small point configurations and hyperplane arrangements in general dimension, including degenerate ones. This extends a number of former works which concentrated on the nondegenerate case and are usually limited to dimension 2 or 3. Our initial study on the complete list for small...