A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Explosion of a collapsing Bose-Einstein condensate

We show that elastic collisions between atoms in a Bose-Einstein condensate with attractive interactions lead to an explosion that ejects a large fraction of the collapsing condensate. We study variationally the dynamics of this explosion and find excellent agreement with recent experiments on magnetically trapped Rubidium-85. We also determine the energy and angular distribution of the ejected atoms during the collapse.Comment: Four pages of ReVTeX and five postscript figure

Cooper pair formation in trapped atomic Fermi gases

We apply the closed time-path formalism to evaluate the dynamics of the BCS transition to the superfluid state in trapped atomic $^6$Li. We find that the Fokker-Planck equation for the probability distribution of the order parameter is, sufficiently close to the critical temperature, identical to the equation that describes the switching on of a single-mode laser.Comment: 4 pages revtex including 1 figur

Elastic and inelastic collisions of 6Li in magnetic and optical traps

We use a full coupled channels method to calculate collisional properties of magnetically or optically trapped ultracold 6Li. The magnetic field dependence of the s-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at B=0.08 T and B=1.98 T. We show that the exact coupled channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.Comment: 4 pages revtex including 4 figures, submitted to PR

Spin domain formation in spinor Bose-Einstein condensation

The spatial structure of the spinor Bose-Einstein condensates with the spin degrees of freedom is analyzed based on the generalized Gross-Pitaevskii equation (GP) in the light of the present spin domain experiment on m_F=\pm 1, and 0 of the hyperfine state F=1 of ^{23}Na atom gases. The GP solutions in three- and one-spatial dimensional cases reproduce the observed spin domain structures, revealing the length scale associated with the existence of the weak interaction of the spin-spin channel, other than the ordinary coherence length related to the density-density channel. The obtained domain structure in GP is compared with the result in Thomas-Fermi approximation. The former solution is found to better describe the observed features than the latter.Comment: 9 pages, 14 figure