Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates
Anno: 2002
Autori: Salasnich L., Parola A., Reatto L.
Affiliazione autori: Univ Milan, Dipartimento Fis, Ist Nazl Fis Mat, Unita Milano, I-20133 Milan, Italy
Abstract: Starting from the three-dimensional (3D) Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent nonpolynomial nonlinear Schrodinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D nonpolynomial Schrodinger equation (2D NPSE) that models disk-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schrodinger-like equations with different polynomial nonlinearities.
Giornale/Rivista: PHYSICAL REVIEW A
Volume: 65 (4) Da Pagina: 043614-1 A: 043614-6
Parole chiavi: ultracold atomsDOI: 10.1103/PhysRevA.65.043614Citazioni: 540dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2024-05-12Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui