9 research outputs found
Two-dimensional scattering and bound states of polar molecules in bilayers
Low-energy two-dimensional scattering is particularly sensitive to the
existence and properties of weakly-bound states. We show that interaction
potentials with vanishing zero-momentum Born approximation lead to an anomalously weak bound state which crucially modifies the
two-dimensional scattering properties. This anomalous case is especially
relevant in the context of polar molecules in bilayer arrangements.Comment: 4 pages, 3 figure
Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model
solitons to generic scalar-field solitons for an infinitely stiff potential.
The static k-lump moduli space C^k/S_k features a natural K"ahler metric
induced from an embedding Grassmannian. The moduli-space dynamics is blind
against adding a WZW-like term to the sigma-model action and thus also applies
to the integrable U(1) Ward model. For the latter's two-soliton motion we
compare the exact field configurations with their supposed moduli-space
approximations. Surprisingly, the two do not match, which questions the
adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE