1 Soliton dynamics in Soliton dynamics in a trapped a trapped condensate condensate Lev Pitaevskii Lev Pitaevskii Kapitza Unstitute for Kapitza Unstitute for Physical Problems; Physical Problems; University of Trento University of Trento Nizhniy Novgorod, July Nizhniy Novgorod, July 2007 2007
Soliton dynamics in a trapped condensate. Lev Pitaevskii Kapitza Unstitute for Physical Problems; University of Trento Nizhniy Novgorod, July 2007. Equation for the condensate wave function. “Grey” soliton in an uniform condensate. Burger et al., 1999. Solitons in BEC. - PowerPoint PPT Presentation
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Soliton dynamics in Soliton dynamics in a trapped a trapped
condensatecondensateLev PitaevskiiLev Pitaevskii
Kapitza Unstitute for Kapitza Unstitute for Physical Problems;Physical Problems;
University of TrentoUniversity of Trento
Nizhniy Novgorod, July Nizhniy Novgorod, July 20072007
2
Equation for the condensate Equation for the condensate wave functionwave function
2
2
22
,,
(1961) skiiL.P.Pitaev (1961), Gross E.P.
length scattering theis ,04
2
txtxn
aam
g
xUgmt
i
3
““Grey” soliton in an uniform Grey” soliton in an uniform condensatecondensate
(1971) Tsuzuki T.
,,,
tahn
2
2min22
c
v
n
n
m
gncvcuvttX
tXxmu
c
u
c
vintXx
4
Burger et al., 1999
5
Solitons in BECSolitons in BEC
Engels and Atherton, 2007
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Energy of a solitonEnergy of a soliton
potentialchemicaltheis
)/(
3
4
3
4
2
2
32/322
mc
vmEE
ug
mvcm
gE
ss
s
7
"Number of atoms" in a "Number of atoms" in a solitonsoliton
s
s
s
EN
ug
dxnN22
8
Landau dynamic of Landau dynamic of elementary excitationselementary excitations