Collective oscillations of a trapped quantum gas in low dimensions
Abstract
During last decades the study of quantum or ultracold atomic gases has been the object of significant experimental and theoretical research. These systems exhibit some striking phenomena not present in normal matter, such as Bose-Einstein Condensation, superfluidity and collective oscillations. We focus on collective oscillations in low-dimensional systems whose properties are different with respect to 3-dimension ultracold gases. Our study is a theoretical and unified description of collective modes in different dimensions, based on the hydrodynamic theory and the polytropic equation of state characterized by a power law dependence of pressure on density. It describes collective oscillations for different dimensions, temperature, interaction, statistics and trapping conditions. It yields some limiting results already known in literature but also some new important ones. Special focus will be given to the breathing mode results. Our work, besides being interesting in ultracold-gas domain, it can be very useful for the study of collective oscillations in the inner crust of neutron stars.