Feshbach Molecules in a One-dimensional Optical Lattice

We present the theory of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. Using a two-channel description of the resonance, we derive analytic results for the scattering states inside the continuum band and the discrete bound states outside the band. We identify a Fano resonance profile, and the survival probability of a molecule when swept through the Bloch band of scattering states by varying an applied magnetic field. We discuss how these results may be used to investigate the importance of the structured nature of the continuum in experiments.Comment: 4 pages, 3 figure

Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp

Starting with coupled atom-molecule Boltzmann equations, we develop a simplified model to understand molecule formation observed in recent experiments. Our theory predicts several key features: (1) the effective adiabatic rate constant is proportional to density; (2) in an adiabatic ramp, the dependence of molecular fraction on magnetic field resembles an error function whose width and centroid are related to the temperature; (3) the molecular production efficiency is a universal function of the initial phase space density, the specific form of which we derive for a classical gas. Our predictions show qualitative agreement with the data from [Hodby et al, Phys. Rev. Lett. {\bf{94}}, 120402 (2005)] without the use of adjustable parameters

A Giant Sand Injection Complex: The Upper Jurassic Hareelv Formation of East Greenland

A major intrusive sandstone complex of Late Jurassic age is spectacularly exposed in Jameson land, East Greenland. It is probably the largest in the World, and covers an area of 55x70 km with a thickness of 200–400 m, and forms the Upper Oxfordian–Volgian Hareelv Formation. The complex consists of black basinal mudstones and highly irregular sandstone bodies, dykes and sills. The sand was derived from collapse of the front of sandy shelf-margin wedges, which triggered hyperconcentrated to concentrated density flows, and deposited massive sands further down the slope, at the base-of-slope and in the basin. The sand of some flows was loaded into the slope muds while elsewhere it flowed in steep-sided gullies formed by retrogressive slumping of the slope muds. All sand bodies were liquefied subsequent to burial and the sand was intruded into the surrounding black compacted muds and mudstones. Intrusion took place repeatedly over a long time interval, in environments ranging from very shallow to relatively deep burial, and the primary sediment structures of the sands were generally lost during these processes. It is rarely possible to determine the degree of post-burial remobilization but it ranges from rather small-scale modifications to wholesale liquefaction and out-of-place intrusion of the sand over many tens of metres. Sandstone dykes and sills occur ubiquitously and were emplaced by all combinations of stoping and dilation. The intrusive sand bodies range in dimensions from centimetres to many hundreds of metres. Deposition took place during the most important Mesozoic rift event in East Greenland and the pervasive remobilization and liquefaction of all sand bodies in the Hareelv Formation is interpreted as having been caused mainly by cyclic earthquake shocks. Additional important factors were slope shear stress, build up of pore pressure due to loading, slumping, upwards movement of pore waters expelled from the compacting muds, and also possibly of biogenic and thermogenic gas. The Hareelv Formation is an excellent field analogue for deeply buried hydrocarbon reservoirs, which have been modified by remobilization and injection of the sands

Angular momentum exchange between coherent light and matter fields

Full, three dimensional, time-dependent simulations are presented demonstrating the quantized transfer of angular momentum to a Bose-Einstein condensate from a laser carrying orbital angular momentum in a Laguerre-Gaussian mode. The process is described in terms of coherent Bragg scattering of atoms from a chiral optical lattice. The transfer efficiency and the angular momentum content of the output coupled vortex state are analyzed and compared with a recent experiment.Comment: 4 pages, 4 figure

The Tate conjecture for K3 surfaces over finite fields

Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality, but proofs don't change. Comments still welcom