Numerical methods for Bogoliubov excitations of Bose-Einstein condensates
Date/Time:09 Oct 2019 16:00Venue: S17 #05-11 SR5Speaker: CAI Yongyong, Beijing Computational Science Research CenterNumerical methods for Bogoliubov excitations of Bose-Einstein condensatesWe study the analytical properties and the numerical methods for the Bogoliubov-de Gennes equations (BdGEs) describing the elementary excitation of Bose-Einstein condensates around the mean field ground state, which is governed by the Gross-Pitaevskii equation (GPE). Three numerical methods are proposed to solve the BdGEs, including sine-spectral method, central finite difference method and compact finite difference method. Extensive numerical tests are provided to validate the algorithms and confirm that the sine-spectral method has spectral accuracy in spatial discretization, while the central finite difference method and the compact finite difference method are second-order and fourth-order accurate, respectively. Finally, sine spectral method is extended to study the elementary excitations under optical lattice potential and solve the BdGEs around the first excited states of the GPE.Add to calendar:
