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

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Abstract

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 \({\Delta u - u + u^3 = 0}\) in \({\mathbb{R}^2}\). 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.

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Authors and Affiliations

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan, 430071, People’s Republic of China

    Yujin Guo

  2. IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria

    Robert Seiringer

Authors
  1. Yujin Guo
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  2. Robert Seiringer
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Correspondence to Robert Seiringer.

Additional information

Dedicated to Nassif Ghoussoub on the occasion of his 60th birthday

Y. Guo is partially supported by NSFC Grants 11241003 and 11322104.

R. Seiringer is partially supported by the Natural Science and Engineering Research Council of Canada.

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Guo, Y., Seiringer, R. On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions. Lett Math Phys 104, 141–156 (2014). https://doi.org/10.1007/s11005-013-0667-9

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  • DOI: https://doi.org/10.1007/s11005-013-0667-9

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