Roton-Maxon Spectrum and Stability of Trapped Dipolar Bose-Einstein Condensates

We find that pancake dipolar condensates can exhibit a roton-maxon character of the excitation spectrum, so far observed only in superfluid helium. We also obtain a condition for the dynamical stability of these condensates. The spectrum and the border of instability are tunable by varying the particle density and/or the confining potential. This opens wide possibilities for manipulating the superfluid properties of dipolar condensates.