77 research outputs found
Spectral convexity for attractive SU(2N) fermions
We prove a general theorem on spectral convexity with respect to particle
number for 2N degenerate components of fermions. The number of spatial
dimensions is arbitrary, and the system may be uniform or constrained by an
external potential. We assume only that the interactions are governed by an
SU(2N)-invariant two-body potential whose Fourier transform is negative
definite. The convexity result implies that the ground state is in a
2N-particle clustering phase. We discuss implications for light nuclei as well
as asymmetric nuclear matter in neutron stars.Comment: 10 pages, 2 figures; references adde
Effective Range Corrections to Three-Body Recombination for Atoms with Large Scattering Length
Few-body systems with large scattering length a have universal properties
that do not depend on the details of their interactions at short distances. The
rate constant for three-body recombination of bosonic atoms of mass m into a
shallow dimer scales as \hbar a^4/m times a log-periodic function of the
scattering length. We calculate the leading and subleading corrections to the
rate constant which are due to the effective range of the atoms and study the
correlation between the rate constant and the atom-dimer scattering length. Our
results are applied to 4He atoms as a test case.Comment: 6 pages, 2 figures, improved discussion, final versio
Three-body Recombination of Lithium-6 Atoms with Large Negative Scattering Lengths
The 3-body recombination rate at threshold for distinguishable atoms with
large negative pair scattering lengths is calculated in the zero-range
approximation. The only parameters in this limit are the 3 scattering lengths
and the Efimov parameter, which can be complex valued. We provide semi-analytic
expressions for the cases of 2 or 3 equal scattering lengths and we obtain
numerical results for the general case of 3 different scattering lengths. Our
general result is applied to the three lowest hyperfine states of Lithium-6
atoms. Comparisons with recent experiments provide indications of loss features
associated with Efimov trimers near the 3-atom threshold.Comment: 4 pages, 4 figures, agrees with published versio
Efimov Physics in 6Li Atoms
A new narrow 3-atom loss resonance associated with an Efimov trimer crossing
the 3-atom threshold has recently been discovered in a many-body system of
ultracold 6Li atoms in the three lowest hyperfine spin states at a magnetic
field near 895 G. O'Hara and coworkers have used measurements of the 3-body
recombination rate in this region to determine the complex 3-body parameter
associated with Efimov physics. Using this parameter as the input, we calculate
the universal predictions for the spectrum of Efimov states and for the 3-body
recombination rate in the universal region above 600 G where all three
scattering lengths are large. We predict an atom-dimer loss resonance at (672
+/- 2) G associated with an Efimov trimer disappearing through an atom-dimer
threshold. We also predict an interference minimum in the 3-body recombination
rate at (759 +/- 1) G where the 3-spin mixture may be sufficiently stable to
allow experimental study of the many-body system.Comment: 27 pages, 9 figures, REVTeX4, published versio
Range Corrections to Three-Body Observables near a Feshbach Resonance
A non-relativistic system of three identical particles will display a rich
set of universal features known as Efimov physics if the scattering length a is
much larger than the range l of the underlying two-body interaction. An
appropriate effective theory facilitates the derivation of both results in the
|a| goes to infinity limit and finite-l/a corrections to observables of
interest. Here we use such an effective-theory treatment to consider the impact
of corrections linear in the two-body effective range, r_s on the three-boson
bound-state spectrum and recombination rate for |a| much greater than |r_s|. We
do this by first deriving results appropriate to the strict limit |a| goes to
infinity in coordinate space. We then extend these results to finite a using
once-subtracted momentum-space integral equations. We also discuss the
implications of our results for experiments that probe three-body recombination
in Bose-Einstein condensates near a Feshbach resonance.Comment: 28 pages, 3 figure
Few-body physics in effective field theory
Effective Field Theory (EFT) provides a powerful framework that exploits a
separation of scales in physical systems to perform systematically improvable,
model-independent calculations. Particularly interesting are few-body systems
with short-range interactions and large two-body scattering length. Such
systems display remarkable universal features. In systems with more than two
particles, a three-body force with limit cycle behavior is required for
consistent renormalization already at leading order. We will review this EFT
and some of its applications in the physics of cold atoms and nuclear physics.
In particular, we will discuss the possibility of an infrared limit cycle in
QCD. Recent extensions of the EFT approach to the four-body system and N-boson
droplets in two spatial dimensions will also be addressed.Comment: 10 pages, 5 figures, Proceedings of the INT Workshop on "Nuclear
Forces and the Quantum Many-Body Problem", Oct. 200
Physicochemical and Functional Properties of Extruded Sorghum‐Based Bean Analog
The objective of this study was to develop and evaluate the physicochemical and functional properties of a bean like product made from cold extrusion of sorghum, soy and wheat flours. Formulated samples comprised of sorghum (25–70%), wheat (0–35%) and soy (30–50%) flours. The degree of gelatinization ranged from 54.1 to 93.6%. Pasting curves showed minimal starch damage with peak and final viscosities in the range of 456.0–1138.5 and 297–584 cP, respectively. Textural properties of the extrudates were significantly impacted by starch content and cooking time. There was significant cooking loss due to poor binding properties of the extrudates. Cooking the product for 30 min after 2 h soaking gave comparable hardness to cooked navy bean. Texture profile analysis showed that mostly starch-based ingredients contributed to hardness and cohesiveness, while formulations high in protein showed increased adhesiveness and gumminess
Four-boson scale near a Feshbach resonance
We show that an independent four-body momentum scale drives the
tetramer binding energy for fixed trimer energy (or three-body scale
) and large scattering length (). The three- and four-body forces
from the one-channel reduction of the atomic interaction near a Feshbach
resonance disentangle and . The four-body independent
scale is also manifested through a family of Tjon-lines, with slope given by
for . There is the possibility of a new
renormalization group limit cycle due to the new scale
Universality in Few-Body Systems
Low-energy universality in atomic few-body systems as a result of a large
two-body scattering length has gained a lot of attention recently. Here, I
discuss recent progress in describing the three-body recombination of cold
atoms in terms of a finite set of universal scaling functions and review
results for the recombination length of cesium-133 atoms obtained with these
functions. Furthermore, I will consider the inclusion of effective range
corrections and the relevance for further calculations in atomic and nuclear
physics.Comment: Plenary talk at 20th European Conference on Few-Body Problems in
Physics (EFB 20), Pisa, Italy, 10-14 Sep 2007, FBS style, 2 figue
Universal low-energy properties of three two-dimensional particles
Universal low-energy properties are studied for three identical bosons
confined in two dimensions. The short-range pair-wise interaction in the
low-energy limit is described by means of the boundary condition model. The
wave function is expanded in a set of eigenfunctions on the hypersphere and the
system of hyper-radial equations is used to obtain analytical and numerical
results. Within the framework of this method, exact analytical expressions are
derived for the eigenpotentials and the coupling terms of hyper-radial
equations. The derivation of the coupling terms is generally applicable to a
variety of three-body problems provided the interaction is described by the
boundary condition model. The asymptotic form of the total wave function at a
small and a large hyper-radius is studied and the universal logarithmic
dependence in the vicinity of the triple-collision point is
derived. Precise three-body binding energies and the scattering length
are calculated.Comment: 30 pages with 13 figure
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