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Existence and Asymptotic Behavior of Minimizers for Rotating Bose-Einstein Condensations in Bounded Domains
Authors
Yongshuai Gao
Shuai Li
Peiye Zhong
Publication date
18 October 2023
Publisher
View
on
arXiv
Abstract
This paper is concerned with the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensations (BECs) with attractive interactions in a bounded domain
D
β
R
2
\mathcal{D}\subset \mathbb{R}^2
D
β
R
2
. It is shown that, there exists a finite constant
a
β
a^*
a
β
, denoting mainly the critical number of bosons in the system, such that the least energy
e
(
a
)
e(a)
e
(
a
)
admits minimizers if and only if
0
<
a
<
a
β
0<a<a^*
0
<
a
<
a
β
, no matter the trapping potential
V
(
x
)
V(x)
V
(
x
)
rotates at any velocity
Ξ©
β₯
0
\Omega\geq0
Ξ©
β₯
0
. This is quite different from the rotating BECs in the whole plane case, where the existence conclusions depend on the value of
Ξ©
\Omega
Ξ©
(cf. \cite[Theorem 1.1]{GLY}). Moreover, by establishing the refined estimates of the rotation term and the least energy, we also analyze the mass concentration behavior of minimizers in a harmonic potential as
a
β
a
β
a\nearrow a^*
a
β
a
β
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oai:arXiv.org:2310.11928
Last time updated on 06/01/2024