3,052 research outputs found
Strong contraction of the representations of the three dimensional Lie algebras
For any Inonu-Wigner contraction of a three dimensional Lie algebra we
construct the corresponding contractions of representations. Our method is
quite canonical in the sense that in all cases we deal with realizations of the
representations on some spaces of functions; we contract the differential
operators on those spaces along with the representation spaces themselves by
taking certain pointwise limit of functions. We call such contractions strong
contractions. We show that this pointwise limit gives rise to a direct limit
space. Many of these contractions are new and in other examples we give a
different proof
America\u27s Problems, Present and Future
Never was this country faced with such grave danger. Yet we seem to be devoting more of our energies to fighting among ourÂselves than to fighting the enemy. The truly terrible danger that could overwhelm us is being largely overlooked
Present and Future National Objectives
Admiral Beary has asked me to talk to you on the subject of strategy. I certainly am not equipped to discuss strategy as it relates to specific weapons or to the role of the different services or even to the military importance of the atomic bomb. Since World War One, however, I have studied the inter-relationships of war and peace and some of my thoughts in this regard may inÂterest you
Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation
We present new singular solutions of the biharmonic nonlinear Schrodinger
equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions
collapse with the quasi self-similar ring profile, with ring width L(t) that
vanishes at singularity, and radius proportional to L^\alpha, where
\alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is
1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4.
These solutions are analogous to the ring-type solutions of the nonlinear
Schrodinger equation.Comment: 21 pages, 13 figures, research articl
Single vortex fluctuations in a superconducting chip as generating dephasing and spin flips in cold atom traps
We study trapping of a cold atom by a single vortex line in an extreme type
II superconducting chip, allowing for pinning and friction. We evaluate the
atom's spin flip rate and its dephasing due to the vortex fluctuations in
equilibrium and find that they decay rapidly when the distance to the vortex
exceeds the magnetic penetration length. We find that there are special spin
orientations, depending on the spin location relative to the vortex, at which
spin dephasing is considerably reduced while perpendicular directions have a
reduced spin flip rate. We also show that the vortex must be perpendicular to
the surface for a general shape vortex.Comment: 6 pages, 4 figure
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