41,801 research outputs found
Reversal of the circulation of a vortex by quantum tunneling in trapped Bose systems
We study the quantum dynamics of a model for a vortex in a Bose gas with
repulsive interactions in an anisotropic, harmonic trap. By solving the
Schr\"odinger equation numerically, we show that the circulation of the vortex
can undergo periodic reversals by quantum-mechanical tunneling. With increasing
interaction strength or particle number, vortices become increasingly stable,
and the period for reversals increases. Tunneling between vortex and antivortex
states is shown to be described to a good approximation by a superposition of
vortex and antivortex states (a Schr\"odinger cat state), rather than the
mean-field state, and we derive an analytical expression for the oscillation
period. The problem is shown to be equivalent to that of the two-site Bose
Hubbard model with attractive interactions.Comment: 5 pages, 5 figures; published in Phys. Rev. A, Rapid Communication
The Weak and Strong Lefschetz Properties for Artinian K-Algebras
Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where
char K = 0. Then A has the Weak Lefschetz property if there is an element ell
of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has
maximal rank, for every i, and A has the Strong Lefschetz property if times
ell^d : A_i --> A_{i+d} has maximal rank for every i and d.
The main results obtained in this paper are the following.
1) EVERY height three complete intersection has the Weak Lefschetz property.
(Our method, surprisingly, uses rank two vector bundles on P^2 and the
Grauert-Mulich theorem.)
2) We give a complete characterization (including a concrete construction) of
the Hilbert functions that can occur for K-algebras with the Weak or Strong
Lefschetz property (and the characterization is the same one).
3) We give a sharp bound on the graded Betti numbers (achieved by our
construction) of Artinian K-algebras with the Weak or Strong Lefschetz property
and fixed Hilbert function. This bound is again the same for both properties.
Some Hilbert functions in fact FORCE the algebra to have the maximal Betti
numbers.
4) EVERY Artinian ideal in K[x,y] possesses the Strong Lefschetz property.
This is false in higher codimension.Comment: To appear in J. Algebr
Electron screening in the liquid-gas mixed phases of nuclear matter
Screening effects of electrons on inhomogeneous nuclear matter, which
includes spherical, slablike, and rodlike nuclei as well as spherical and
rodlike nuclear bubbles, are investigated in view of possible application to
cold neutron star matter and supernova matter at subnuclear densities. Using a
compressible liquid-drop model incorporating uncertainties in the surface
tension, we find that the energy change due to the screening effects broadens
the density region in which bubbles and nonspherical nuclei appear in the phase
diagram delineating the energetically favorable shape of inhomogeneous nuclear
matter. This conclusion is considered to be general since it stems from a
model-independent feature that the electron screening acts to decrease the
density at which spherical nuclei become unstable against fission and to
increase the density at which uniform matter becomes unstable against proton
clustering.Comment: 12 pages, 8 figures, accepted for publication in Physical Review
A study of electronic packages environmental control systems and vehicle thermal systems integration Quarterly report, Nov. 1966 - Jan. 1967
Heat balances of combined astrionic equipment and thermal conditioning subsystem of environmental control system, and vehicle configuration
Transition from Band insulator to Bose-Einstein Condensate superfluid and Mott State of Cold Fermi Gases with Multiband Effects in Optical Lattices
We study two models realized by two-component Fermi gases loaded in optical
lattices. We clarify that multi-band effects inevitably caused by the optical
lattices generate a rich structure, when the systems crossover from the region
of weakly bound molecular bosons to the region of strongly bound atomic bosons.
Here the crossover can be controlled by attractive fermion interaction. One of
the present models is a case with attractive fermion interaction, where an
insulator-superfluid transition takes place. The transition is characterized as
the transition between a band insulator and a Bose-Einstein condensate (BEC)
superfluid state. Differing from the conventional BCS superfluid transition,
this transition shows unconventional properties. In contrast to the one
particle excitation gap scaled by the superfluid order parameter in the
conventional BCS transition, because of the multi-band effects, a large gap of
one-particle density of states is retained all through the transition although
the superfluid order grows continuously from zero. A reentrant transition with
lowering temperature is another unconventionality. The other model is the case
with coexisting attractive and repulsive interactions. Within a mean field
treatment, we find a new insulating state, an orbital ordered insulator. This
insulator is one candidate for the Mott insulator of molecular bosons and is
the first example that the orbital internal degrees of freedom of molecular
bosons appears explicitly. Besides the emergence of a new phase, a coexisting
phase also appears where superfluidity and an orbital order coexist just by
doping holes or particles. The insulating and superfluid particles show
differentiation in momentum space as in the high-Tc cuprate superconductors.Comment: 13 pages, 10 figure
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