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SUMMARY:Modeling\, analysis and simulation for degenerate dipolar quantum 
 gas - Weizhu Bao (National University of Singapore)
DTSTART:20220527T080000Z
DTEND:20220527T090000Z
UID:TALK173636@talks.cam.ac.uk
DESCRIPTION:In this talk\, I will present our recent work on mathematical 
 models\, asymptotic analysis and numerical simulation for degenerate dipol
 ar quantum gas. As preparatory steps\, I begin with the three-dimensional 
 Gross-Pitaevskii equation with a long-range dipolar interaction potential 
 which is used to model the degenerate dipolar quantum gas and reformulate 
 it as a Gross-Pitaevskii-Poisson type system by decoupling the two-body di
 polar interaction potential which is highly singular into short-range (or 
 local) and long-range interactions (or repulsive and attractive interactio
 ns). Based on this new mathematical formulation\, we prove rigorously exis
 tence and uniqueness as well as nonexistence of the ground states\, and di
 scuss the existence of global weak solution and finite time blowup of the 
 dynamics in different parameter regimes of dipolar quantum gas. In additio
 n\, a backward Euler sine pseudospectral method is presented for computing
  the ground states and a time-splitting sine pseudospectral method is prop
 osed for computing the dynamics of dipolar BECs. Due to the adoption of ne
 w mathematical formulation\, our new numerical methods avoid evaluating in
 tegrals with high singularity and thus they are more efficient and accurat
 e than those numerical methods currently used in the literatures for solvi
 ng the problem. In addition\, new mathematical formulations in two-dimensi
 ons and one dimension for dipolar quantum gas are obtained when the extern
 al trapping potential is highly confined in one or two directions. Numeric
 al results are presented to confirm our analytical results and demonstrate
  the efficiency and accuracy of our numerical methods. Some interesting ph
 ysical phenomena are discussed too.
LOCATION:Seminar Room 1\, Newton Institute
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