Abstract
AbstractThis chapter develops the theory of weakly interacting nonuniform Bose gases at zero temperature. Interaction effects are accounted for by a single coupling constant fixed by the value of the s-wave scattering length. The nonlinear Gross–Pitaevskii equation is derived in both the stationary and time-dependent cases. The irrotational nature of the flow and the crucial role played by the chemical potential are highlighted. The classical nature of the equation is emphasized and the analogy with the Maxwell equations of classical electrodynamics is pointed out. The stationary solutions of the Gross–Pitaevskii equation, corresponding to quantized vortex lines, vortex rings, and solitons, are discussed. The time-dependent solutions corresponding to small-amplitude oscillations are derived and the corresponding dispersion relation is shown to coincide with the predictions of Bogoliubov theory for uniform media. The Thomas–Fermi limit is also discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
