Condition for tripartite entanglement

We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley hyper-determinant, and its six associated $2 \times 2$ subdeterminants. In particular we show that this classification provides a necessary and sufficient condition for separability.Comment: 8 pages, to appear in the Proceedings of "Quantum Theory and Symmetries 7", Prague, Aug 7-13, 201

Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na, $^{39}$K, and $^{87}$Rb can be either a ferromagnetic or a "polar" state, depending on the scattering lengths in different angular momentum channel. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of superfluid $^{3}$He-A. Current estimates of scattering lengths suggest that the ground states of $^{23}$Na and $^{87}$Rb condensate are a polar state and a ferromagnetic state respectively.Comment: 11 pages, no figures. email : [email protected]

An X-ray/optical study of the geometry and dynamics of MACS J0140.0-0555, a massive post-collision cluster merger

We investigate the physical properties, geometry and dynamics of the massive cluster merger MACS J0140.0-0555 (z=0.451) using X-ray and optical diagnostics. Featuring two galaxy overdensities separated by about 250 kpc in projection on the sky, and a single peak in the X-ray surface brightness distribution located between them, MACS J0140.0-0555 shows the tell-tale X-ray/optical morphology of a binary, post-collision merger. Our spectral analysis of the X-ray emission, as measured by our Chandra ACIS-I observation of the system, finds the intra-cluster medium to be close to isothermal (~8.5 keV) with no clear signs of cool cores or shock fronts. Spectroscopic follow-up of galaxies in the field of MACS J0140.0-0555 yields a velocity dispersion of 875 (+70/-100) km/s (n_z=66) and no significant evidence of bimodality or substructure along the line of sight. In addition, the difference in radial velocity between the brightest cluster galaxies of the two sub-clusters of 144+/-25 km/s is small compared to typical collision velocities of several 1000 km/s. A strongly lensed background galaxy at z=0.873 (which features variable X-ray emission from an active nucleus) provides the main constraint on the mass distribution of the system. We measure M(<75 kpc) = (5.6+/- 0.5)*10^13 M_sun for the north-western cluster component and a much less certain estimate of (1.5-3)*10^13 M_sun for the south-eastern subcluster. These values are in good agreement with our X-ray mass estimates which yield a total mass of MACS J0140.0-0555 of M(<r_500) ~ (6.8-9.1)*10^14 M_sun. ......Comment: 11 pages, 8 figures, and 2 tables. Accepted for publication in MNRA