Low-energy effective field theory of nonrelativistic superfluids

The aim of the proposed project is to study the low-energy properties of Bose-Einstein condensation (BEC) in a gas of nonrelativistic particles using the modern techniques of effective field theory. While the physics of BEC and quantum liquids in general has been well understood for decades, only recently has one started to analyze it using the powerful methods of effective field theory (EFT). These often allow to rederive well known results in an efficient and systematic way and thereby provide deeper in sight into the physics itself. In high-energy physics the EFT techniques have been employed to study the low-energy physics of spontaneous symmetry breaking, in particular BEC of pseudoscalar mesons in the phases of extremely dense quark matter. However, a similar analysis in the context of the original, nonrelativistic BEC seems to be missing. Based on the previous work done in literature, we will show that the knowledge of the equation of state alone can be utilized to construct the low-energy effective action for the Bogoliubov collective modes in BEC. We will then investigate the interactions among the soft modes which lead to the Beliaev damping at zero temperature and the Landau damping at nonzero temperature, and give rise to transport phenomena. T he low-energy effective theory here provides a microscopic input into the phenomenological Boltzmann hydrodynamic description of the system. When time permits, we will apply the same strategy to the so-called BCS-BEC crossover in the attractive gas of fer mions. Here the nature of the collective modes changes as one switches from the weakly attractive BCS-like regime to the strongly attractive BEC-like one. Of special importance is the intermediate, unitary regime, which displays highly nontrivial, yet uni versal dynamics, and thus seems particularly suitable for the application of EFT methods.