On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions
By Yujin Guo, Robert Seiringer. 2013
261 citations recorded by the source corpus.
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 $${a < a^* = \|Q\|_2^2}$$a<a∗=‖Q‖22, where Q is the unique positive radial solution of $${\Delta u - u + u^3 = 0}$$Δu-u+u3=0 in $${\mathbb{R}^2}$$R2. 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.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/de4223f7b5f7e2fd11f0323505e1b07d2b555113
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
Citations in the corpus
- Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities (2021, background): “As pointed out in [29, 36], the studies on (1.”
- Mass minimizers and concentration for nonlinear Choquard equations in $\R^N$ (2015, methodology): “The method in [7] by using the perturbation term ∫ RN V (x)u(2) to remove the local nonlinearity term does not work in our cases.”
- The existence of normalized solutions for L2-critical constrained problems related to Kirchhoff equations (2014, background): “, [8], where V (x) is locally bounded satisfying V (x) ≥ 0 and lim |x|→+∞ V (x) = +∞.”
- Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials (2014, methodology): “Part (i) of the above theorem is just Theorem 1 of [12].”