Two-dimensional Lorentz-violating Chern-Simons-like action

We demonstrate generation of the two-dimensional Chern-Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.Comment: 10 pages, references added, version accepted to Physics Letters

Ultradilute low-dimensional liquids

We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.Comment: published version + supplemental materia