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• W3100960834 abstract "We study the collapse of a many-body system which is used to model two-component Bose-Einstein condensates with attractive intra-species interactions and either attractive or repulsive inter-species interactions. Such a system consists a mixture of two different species for $N$ identical bosons in $mathbb R^2$, interacting with potentials rescaled in the mean-field manner $-N^{2beta-1}w^{(sigma)}(N^{beta}x)$ with $int_{mathbb R^{2}}w^{(sigma)}(x){rm d}x=1$. Assuming that $0<beta<1/2$, we first show that the leading order of the quantum energy is captured correctly by the Gross-Pitaevskii energy. Secondly, we investigate the blow-up behavior of the quantum energy as well as the ground states when $Ntoinfty$ and either the total interaction strength of intra-species and inter-species or the strengths of intra-species interactions of each component approaches sufficiently slowly a critical value, which is the critical strength for the focusing Gross-Pitaevskii functional. We prove that the many-body ground states fully condensate on the (unique) Gagliardo-Nirenberg solution." @default.
• W3100960834 created "2020-11-23" @default.
• W3100960834 creator A5053299500 @default.
• W3100960834 date "2020-04-30" @default.
• W3100960834 modified "2023-10-18" @default.
• W3100960834 title "Blow-up profile of 2D focusing mixture Bose gases" @default.
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• W3100960834 doi "https://doi.org/10.1007/s00033-020-01302-y" @default.
• W3100960834 hasPublicationYear "2020" @default.
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