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Comments on Worldsheet Description of the Omega Background
Nekrasov's partition function is defined on a flat bundle of R^4 over S^1
called the Omega background. When the fibration is self-dual, the partition
function is known to be equal to the topological string partition function,
which computes scattering amplitudes of self-dual gravitons and graviphotons in
type II superstring compactified on a Calabi-Yau manifold. We propose a
generalization of this correspondence when the fibration is not necessarily
self-dual.Comment: 11 page
Motion of a condensate in a shaken and vibrating harmonic trap
The dynamics of a Bose-Einstein condensate (BEC) in a time-dependent harmonic
trapping potential is determined for arbitrary variations of the position of
the center of the trap and its frequencies. The dynamics of the BEC wavepacket
is soliton-like. The motion of the center of the wavepacket, and the spatially
and temporally dependent phase (which affects the coherence properties of the
BEC) multiplying the soliton-like part of the wavepacket, are analytically
determined.Comment: Accepted for publication in J. Phys. B: At Mol Opt Phy
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