On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions

We consider two-dimensional Bose–Einstein condensates with attractive interaction, described by the Gross–Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies a < a ∗ = ‖ Q ‖ 2 2 , where Q is the unique positive radial solution of Δ u - u + u 3 =...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 104; no. 2; pp. 141 - 156
Main Authors Guo, Yujin, Seiringer, Robert
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.02.2014
Subjects
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
46N50
mass concentration
symmetry breaking
Bose–Einstein condensation
Gross–Pitaevskii functional
attractive interactions
82D50
35Q40
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Summary:We consider two-dimensional Bose–Einstein condensates with attractive interaction, described by the Gross–Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies a < a ∗ = ‖ Q ‖ 2 2 , where Q is the unique positive radial solution of Δ u - u + u 3 = 0 in R 2 . We present a detailed analysis of the behavior of minimizers as a approaches a *, where all the mass concentrates at a global minimum of the trapping potential.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-013-0667-9