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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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1
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
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““Grey” soliton in an uniform Grey” soliton in an uniform condensatecondensate
(1971) Tsuzuki T.
,,,
tahn
2
2min22
c
v
n
n
m
gncvcuvttX
tXxmu
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Burger et al., 1999
5
Solitons in BECSolitons in BEC
Engels and Atherton, 2007
6
Energy of a solitonEnergy of a soliton
potentialchemicaltheis
)/(
3
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3
4
2
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"Number of atoms" in a "Number of atoms" in a solitonsoliton
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Landau dynamic of Landau dynamic of elementary excitationselementary excitations
constnH
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Weakly inhomogeneous Weakly inhomogeneous condensatecondensate
222
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onconservati Energy
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Local density approximationLocal density approximation
2004 ,Pitaevskii L. Konotop, V.
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Density perturbationDensity perturbation
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or if validis theory The
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Simple physical Simple physical interpretationinterpretation
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BEC condensateBEC condensate
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Effective energyEffective energy
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Snake instability of a flat Snake instability of a flat solitonsoliton
1988 Turitsyn, S. and Kuznetsov E. 1975, ; ZakharovV.
1970; li,Petviashvi V. and Kadomtsev B.
3/:BEC
,
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22
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00
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Modified EquationsModified Equations
(2002) al.,et Salasnich L.
t confinemen radialin weak Solitons1/2,
.0point near the gas Bose 1D 2.
0
2*
2*2
22
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g
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(2005) ,Pitaevskii L. Konotop, V.
frequency trap theof change Adiabatic
7.1,2/1
3.2,2
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equations. modifiedin solitons Slow