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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Modeling\, analysis and simulation for degenerate
dipolar quantum gas - Weizhu Bao (National Univers
ity of Singapore)
DTSTART;TZID=Europe/London:20220527T090000
DTEND;TZID=Europe/London:20220527T100000
UID:TALK173636AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173636
DESCRIPTION:In this talk\, I will present our recent work on m
athematical models\, asymptotic analysis and numer
ical simulation for degenerate dipolar quantum gas
. As preparatory steps\, I begin with the three-di
mensional Gross-Pitaevskii equation with a long-ra
nge dipolar interaction potential which is used to
model the degenerate dipolar quantum gas and refo
rmulate it as a Gross-Pitaevskii-Poisson type syst
em by decoupling the two-body dipolar interaction
potential which is highly singular into short-rang
e (or local) and long-range interactions (or repul
sive and attractive interactions). Based on this n
ew mathematical formulation\, we prove rigorously
existence and uniqueness as well as nonexistence o
f the ground states\, and discuss the existence of
global weak solution and finite time blowup of th
e dynamics in different parameter regimes of dipol
ar quantum gas. In addition\, a backward Euler sin
e pseudospectral method is presented for computing
the ground states and a time-splitting sine pseud
ospectral method is proposed for computing the dyn
amics of dipolar BECs. Due to the adoption of new
mathematical formulation\, our new numerical metho
ds avoid evaluating integrals with high singularit
y and thus they are more efficient and accurate th
an those numerical methods currently used in the l
iteratures for solving the problem. In addition\,
new mathematical formulations in two-dimensions an
d one dimension for dipolar quantum gas are obtain
ed when the external trapping potential is highly
confined in one or two directions. Numerical resul
ts are presented to confirm our analytical results
and demonstrate the efficiency and accuracy of ou
r numerical methods. Some interesting physical phe
nomena are discussed too.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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