Abstract
We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction ismarkedly different: The Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short-range correlations between the particles we discuss the energetic origin of this difference. Our main calculations are based on Hartree-Fock theory, but we also provide analytic approximations for the magnetostriction effects at zero and finite temperature. Our predictions should be verifiable in current experiments with ultracold polar molecules.