4,152 research outputs found
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
Location and product bundling in the provision of WiFi networks
WiFi promises to revolutionise how and where we access the internet. As WiFi networks are rolled out around the globe, access to the internet will no longer be through fixed networks or unsatisfactory mobile phone connections. Instead access will be through low cost wireless networks at speeds of up to 11Mbps. It is hard not to be impressed by the enthusiasm with which WiFi has been embraced. GREEN, ROSENBUSH, CROKETT and HOLMES (2003) assert that WiFi is a disruptive technology akin to telephones in the 1920s and network computers in the 1990s. WiFi is seen as both an opportunity in its own right, as well as an enabler of opportunities for others. Computer manufacturers are hoping that WiFi will increases sales of their laptops, whilst Microsoft feels that WiFi will result in users upgrading their operating systems to Windows XP. This paper seeks to understand why three companies have sought to provide WiFi
Energy spectra of small bosonic clusters having a large two-body scattering length
In this work we investigate small clusters of bosons using the hyperspherical
harmonic basis. We consider systems with particles interacting
through a soft inter-particle potential. In order to make contact with a real
system, we use an attractive gaussian potential that reproduces the values of
the dimer binding energy and the atom-atom scattering length obtained with one
of the most widely used He-He interactions, the LM2M2 potential. The
intensity of the potential is varied in order to explore the clusters' spectra
in different regions with large positive and large negative values of the
two-body scattering length. In addition, we include a repulsive three-body
force to reproduce the trimer binding energy. With this model, consisting in
the sum of a two- and three-body potential, we have calculated the spectrum of
the four, five and six particle systems. In all the region explored, we have
found that these systems present two bound states, one deep and one shallow
close to the threshold. Some universal relations between the energy
levels are extracted; in particular, we have estimated the universal ratios
between thresholds of the three-, four-, and five-particle continuum using the
two-body gaussia
Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
This is the second paper in a series. In part I we developed deformation
theory of objects in homotopy and derived categories of DG categories. Here we
extend these (derived) deformation functors to an appropriate bicategory of
artinian DG algebras and prove that these extended functors are
pro-representable in a strong sense.Comment: Alexander Efimov is a new co-author of this paper. New material was
added: A_{\infty}-structures, Maurer-Cartan theory for A_{\infty}-algebras.
This allows us to strengthen our main results on the pro-representability of
pseudo-functors coDEF_{-} and DEF_{-}. We also obtain an equivalence between
homotopy and derived deformation functors under weaker hypothese
Three-fermion problems in optical lattices
We present exact results for the spectra of three fermionic atoms in a single
well of an optical lattice. For the three lowest hyperfine states of Li6 atoms,
we find a Borromean state across the region of the distinct pairwise Feshbach
resonances. For K40 atoms, nearby Feshbach resonances are known for two of the
pairs, and a bound three-body state develops towards the positive
scattering-length side. In addition, we study the sensitivity of our results to
atomic details. The predicted few-body phenomena can be realized in optical
lattices in the limit of low tunneling.Comment: 4 pages, 4 figures, minor changes, to appear in Phys. Rev. Let
The Four-Boson System with Short-Range Interactions
We consider the non-relativistic four-boson system with short-range forces
and large scattering length in an effective quantum mechanics approach. We
construct the effective interaction potential at leading order in the large
scattering length and compute the four-body binding energies using the
Yakubovsky equations. Cutoff independence of the four-body binding energies
does not require the introduction of a four-body force. This suggests that two-
and three-body interactions are sufficient to renormalize the four-body system.
We apply the equations to 4He atoms and calculate the binding energy of the 4He
tetramer. We observe a correlation between the trimer and tetramer binding
energies similar to the Tjon line in nuclear physics. Over the range of binding
energies relevant to 4He atoms, the correlation is approximately linear.Comment: 23 pages, revtex4, 5 PS figures, discussion expanded, results
unchange
Anomalies in Quantum Mechanics: the 1/r^2 Potential
An anomaly is said to occur when a symmetry that is valid classically becomes
broken as a result of quantization. Although most manifestations of this
phenomenon are in the context of quantum field theory, there are at least two
cases in quantum mechanics--the two dimensional delta function interaction and
the 1/r^2 potential. The former has been treated in this journal; in this
article we discuss the physics of the latter together with experimental
consequences.Comment: 16 page latex file; to be published in Am. J. Phy
Deformation theory of objects in homotopy and derived categories III: abelian categories
This is the third paper in a series. In part I we developed a deformation
theory of objects in homotopy and derived categories of DG categories. Here we
show how this theory can be used to study deformations of objects in homotopy
and derived categories of abelian categories. Then we consider examples from
(noncommutative) algebraic geometry. In particular, we study noncommutative
Grassmanians that are true noncommutative moduli spaces of structure sheaves of
projective subspaces in projective spaces.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor
changes, a new part (part 3) about noncommutative Grassmanians was adde
- …