Quantum gases of bosons and fermions behave as superfluids, and for parametric excitations, the sample exhibit Faraday Waves, which obey a Mathieu equation. Therefore, to generate them, we need to consider a periodic modulation in a parameter of the system, e.g., the trap frequencies or contact interaction. From the experimental point of view, these excitations are manifested in trapped gas when the density pattern appears. Theoretically, these phenomena have been studied in a variational approximation using mean-field equations. For the case of a Bose-Einstein Condensate, the system is described by the Gross-Pitaevskii equation, and for a Fermi Unitary Gas the Extended Thomas-Fermi model is used. However, we believe that the natural way to study these excitations is using Bogouliubov-de Gennes (BdG) method, where the density modulation generates the excitations (phonons). The usual treatment in this theory is to consider a homogeneous gas. In this context, we present the description of Faraday waves using BdG method. As preliminary results, we consider a homogeneous case with a modulation of the contact interaction.
|Presenter name||Alejandra del Río Lima|
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