1,278 research outputs found
Energies of knot diagrams
We introduce and begin the study of new knot energies defined on knot
diagrams. Physically, they model the internal energy of thin metallic solid
tori squeezed between two parallel planes. Thus the knots considered can
perform the second and third Reidemeister moves, but not the first one. The
energy functionals considered are the sum of two terms, the uniformization term
(which tends to make the curvature of the knot uniform) and the resistance term
(which, in particular, forbids crossing changes). We define an infinite family
of uniformization functionals, depending on an arbitrary smooth function
and study the simplest nontrivial case , obtaining neat normal forms
(corresponding to minima of the functional) by making use of the Gauss
representation of immersed curves, of the phase space of the pendulum, and of
elliptic functions
A Chandra Study of the Effects of a Major Merger on the Structure of Abell 2319
We present an analysis of a Chandra observation of the massive, nearby galaxy
cluster Abell 2319. A sharp surface brightness discontinuity--suggested by
previous, lower angular resolution X-ray imaging--is clearly visible in the
ACIS image. This roughly 300kpc feature suggests that a major merger is taking
place with a significant velocity component perpendicular to the line of sight.
The cluster emission-weighted mean temperature is 11.8+/-0.6kev, somewhat
higher than previous temperature measurements. The Chandra temperature map of
A2319 reveals substructure resembling that anticipated based on hydrodynamic
simulations of cluster mergers. The merger feature shows a pressure change
across the surface brightness discontinuity by a factor of <=2.5. The higher
density side of the front has a lower temperature, suggesting the presence of a
cold front similar to those in many other merging clusters. The velocity of the
front is roughly sonic.
We compare bulk properties of the ICM and galaxies in A2319 to the same
properties in a large sample of clusters as a way of gauging the effects of the
major merger. Interestingly, by comparing A2319 to a sample of 44 clusters
studied with the ROSAT PSPC we find that the X-ray luminosity, isophotal size,
and ICM mass are consistent with the expected values for a cluster of its
temperature; in addition, the K-band galaxy light is consistent with the
light--temperature scaling relation derived from a sample of about 100 clusters
studied with 2MASS. Together, these results indicate either that the merger in
A2319 has not been effective at altering the bulk properties of the cluster, or
that there are large but correlated displacements in these quantities.Comment: 11 pages, 8 figures, ApJ Submitte
Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li
We measure a zero crossing in the scattering length of a mixture of the two
lowest hyperfine states of 6-Li. To locate the zero crossing, we monitor the
decrease in temperature and atom number arising from evaporation in a CO2 laser
trap as a function of magnetic field B. The temperature decrease and atom loss
are minimized for B=528(4) G, consistent with no evaporation. We also present
preliminary calculations using potentials that have been constrained by the
measured zero crossing and locate a broad Feshbach resonance at approximately
860 G, in agreement with previous theoretical predictions. In addition, our
theoretical model predicts a second and much narrower Feshbach resonance near
550 G.Comment: Five pages, four figure
Efficient and robust initialization of a qubit register with fermionic atoms
We show that fermionic atoms have crucial advantages over bosonic atoms in
terms of loading in optical lattices for use as a possible quantum computation
device. After analyzing the change in the level structure of a non-uniform
confining potential as a periodic potential is superimposed to it, we show how
this structure combined with the Pauli principle and fermion degeneracy can be
exploited to create unit occupancy of the lattice sites with very high
efficiency.Comment: 4 pages, 3 figure
Collective excitations in a fermion-fermion mixture with different Fermi surfaces
In this paper, collective excitations in a homogeneous fermion-fermion
mixture with different Fermi surfaces are studied. In the Fermi liquid phase,
the zero-sound velocity is found to be larger than the largest Fermi velocity.
With attractive interactions, the superfluid phase appears below a critical
temperature, and the phase mode is the low-energy collective excitation. The
velocity of the phase mode is proportional to the geometric mean of the two
Fermi velocities. The difference between the two velocities may serve as a tool
to detect the superfluid phase.Comment: 4 pages. To be published in Phys. Rev.
All-optical formation of a Bose-Einstein condensate for applications in scanning electron microscopy
We report on the production of a F=1 spinor condensate of 87Rb atoms in a
single beam optical dipole trap formed by a focused CO2 laser. The condensate
is produced 13mm below the tip of a scanning electron microscope employing
standard all-optical techniques. The condensate fraction contains up to 100,000
atoms and we achieve a duty cycle of less than 10s.Comment: 5 pages, 4 figure
Effective s- and p-Wave Contact Interactions in Trapped Degenerate Fermi Gases
The structure and stability of dilute degenerate Fermi gases trapped in an
external potential is discussed with special emphasis on the influence of s-
and p-wave interactions. In a first step an Effective Contact Interaction for
all partial waves is derived, which reproduces the energy spectrum of the full
potential within a mean-field model space. Using the s- and p-wave part the
energy density of the multi-component Fermi gas is calculated in Thomas-Fermi
approximation. On this basis the stability of the one- and two-component Fermi
gas against mean-field induced collapse is investigated. Explicit stability
conditions in terms of density and total particle number are given. For the
single-component system attractive p-wave interactions limit the density of the
gas. In the two-component case a subtle competition of s- and p-wave
interactions occurs and gives rise to a rich variety of phenomena. A repulsive
p-wave part, for example, can stabilize a two-component system that would
otherwise collapse due to an attractive s-wave interaction. It is concluded
that the p-wave interaction may have important influence on the structure of
degenerate Fermi gases and should not be discarded from the outset.Comment: 18 pages, 11 figures (using RevTEX4
Four-Wave mixing in degenerate Fermi gases: Beyond the undepleted pump approximation
We analyze the full nonlinear dynamics of the four-wave mixing between an
incident beam of fermions and a fermionic density grating. We find that when
the number of atoms in the beam is comparable to the number of atoms forming
the grating, the dephasing of that grating, which normally leads to a decay of
its amplitude, is suppressed. Instead, the density grating and the beam density
exhibit large nonlinear coupled amplitude oscillations. In this case four-wave
mixing can persist for much longer times compared to the case of negligible
back-action. We also evaluate the efficiency of the four-wave mixing and show
that it can be enhanced by producing an initial density grating with an
amplitude that is less than the maximum value. These results indicate that
efficient four-wave mixing in fermionic alkali gases should be experimentally
observable.Comment: 9 pages, 8 figure
Rapid sympathetic cooling to Fermi degeneracy on a chip
Neutral fermions present new opportunities for testing many-body condensed
matter systems, realizing precision atom interferometry, producing ultra-cold
molecules, and investigating fundamental forces. However, since their first
observation, quantum degenerate Fermi gases (DFGs) have continued to be
challenging to produce, and have been realized in only a handful of
laboratories. In this Letter, we report the production of a DFG using a simple
apparatus based on a microfabricated magnetic trap. Similar approaches applied
to Bose-Einstein Condensation (BEC) of 87Rb have accelerated evaporative
cooling and eliminated the need for multiple vacuum chambers. We demonstrate
sympathetic cooling for the first time in a microtrap, and cool 40K to Fermi
degeneracy in just six seconds -- faster than has been possible in conventional
magnetic traps. To understand our sympathetic cooling trajectory, we measure
the temperature dependence of the 40K-87Rb cross-section and observe its
Ramsauer-Townsend reduction.Comment: 5 pages, 4 figures (v3: new collision data, improved atom number
calibration, revised text, improved figures.
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