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 $A=2,3,4,5,6$ 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 $^4$He-$^4$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 $A-1$ 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