Laser traps for radioactive isotopes

The techniques of laser cooling and trapping now make it possible to observe large samples of stable atoms in a small volume at low temperature. This capability was recently extended to radioactive isotopes. This opens up new opportunities for the investigation of fundamental symmetries through measurements using radioactive atoms. In this paper we will discuss several fundamental measurements in atomic systems and how the ability to trap radioactive atoms will play an important role in improving the precision of such measurements. Measurements of the effects of the weak interaction are of particular note since they are becoming quite precise. In particular, we will describe in detail the system developed at Stony Brook to trap radioactive alkali atoms and measure weak interaction effects in francium isotopes.     

Three-dimensional wake potential in a streaming dusty plasma

The oscillatory wake potential for a slowly moving or static test dust particulate in a finite temperature, collisionless and unmagnetized dusty plasma with a continuous flow of ions and dust particles has been studied. The collective resonant interaction of the moving test particle with the low-frequency and low-phase-velocity dust-acoustic mode is the origin of the periodic attractive force between the like polarity particulates along and perpendicular to the streaming ions and dust grains resulting into dust-Coulomb crystal formation. This wake potential can explain the three-dimensional dust-Coulomb crystal formation in the laboratory conditions.     

Axialisation, cooling and quenching of ions in a Penning trap

On the basis of a macroscopic ground state population it was argued recently that Bose-Einstein condensation should occur in a one-dimensional harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is well-defined. We show that in both systems although the ground state populations show sharp onsets at the critical temperature, the behaviour of the specific heat is analytic, which proves the absence of a phase transition in these systems. Received: 17 February 1997 / Revised: 3 September 1997 / Accepted: 13 October 1997     

The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graphs on four vertices representing entangled states. It turns out that for these graphs the value of the concurrence is exactly fractional. Received July 28, 2004     

Inverse geophysical problems for some noncompactly supported inhomogeneities

Let[²+k²n(x₁,x₃)]u(x₁,x₂,x₃)=−δ(x₁,y₁δ(x₂,y₂)δ(x₃,y₃) in R³₊. Assume that u(x₁,x₂,x₃=0,y₁,y₂=0,y₃=0,k) is measured at the plane P {x:x₃=0} for all positions of the source on the line y = (y₁,y₂ = 0,y₃ = 0), -∞ < y₁ < ∞, and receiver on the plane(x₁,x₂,x₃ − <x₁,x₂ < ∞, and for low-frequencies 0 < k <k₀, k₀ > 0 is an arbitrary small wave number. Assume thatn(x₁,x₃) is an arbitrary bounded piecewise-continuous function. The basic result is: the above low-frequency surface data determinen(x₁,x₃)uniquely.     

Stability measurements on cored cables in normal and superfluid helium

The relative stability of LHC type cables has been measured by the direct heating of one of the individual strands with a short duration current pulse. The minimum energy required to initiate a quench has been determined for a number of cables which have a central core to increase the effective inter-strand cross-over resistance. Experiments were performed in both normal helium at 4.4 K and superfluid at 1.9 K. Conductors in general are less stable at the lower temperature when measured at the same fraction of critical current. Results show that the cored-cables, even when partially filled with solder or with a ‘porous-metal' filler exhibit a relatively low stability at currents close to the critical current. It is speculated that the high inter-strand electrical and thermal resistance inherent in these cables may affect the stability at high currents.