Heating rates for an atom in a far-detuned optical lattice

We calculate single atom heating rates in a far detuned optical lattice, in connection with recent experiments. We first derive a master equation, including a realistic atomic internal structure and a quantum treatment of the atomic motion in the lattice. The experimental feature that optical lattices are obtained by superimposing laser standing waves of different frequencies is also included, which leads to a micromotional correction to the light shift that we evaluate. We then calculate, and compare to experimental results, two heating rates, the "total" heating rate (corresponding to the increase of the total mechanical energy of the atom in the lattice), and the ground bande heating rate (corresponding to the increase of energy within the ground energy band of the lattice).Comment: 11 pages, 3 figures, 1 tabl

Resonance of basis-conjugating automorphism groups

We determine the structure of the first resonance variety of the cohomology ring of the group of automorphisms of a finitely generated free group which act by conjugation on a given basis.Comment: 7 page

On the cohomology of discriminantal arrangements and Orlik-Solomon algebras

We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in an arbitrary complex rank one local system. We also establish the relationship between the cohomology support loci of the complement of a discriminantal arrangement and the resonant varieties of its Orlik-Solomon algebra.Comment: LaTeX2e, 16 pages, to appear in Singularities and Arrangements, Sapporo-Tokyo 1998, Advanced Studies in Pure Mathematic

Cohomology rings of almost-direct products of free groups

An almost-direct product of free groups is an iterated semidirect product of finitely generated free groups in which the action of the constituent free groups on the homology of one another is trivial. We determine the structure of the cohomology ring of such a group. This is used to analyze the topological complexity of the associated Eilenberg-Mac Lane space.Comment: 16 page

The effect of zonal gradients of sea surface temperature on the Indian Ocean winter monsoon

Several global climate simulations by the 7-layer, 8 x 10 GISS climate model were designed to test the contributions of various surface boundary conditions to the global climate. The model was run with the sun fixed at a perpetual January. In a comparison of run #5, in which realistic January surface boundary conditions were used, with run #4, which was the same except that a zonally symmetric climatological January sea surface temperature (SST) field was used, one of the results was that run #5 provided a better simulation of the Indian Ocean monsoon. A further comparison of the wind fields over the Indian Ocean that were generated by these two model runs is presented