Ground states of attractive Bose gases in rotating anharmonic traps

作者：Guo, Yujin^*; Li, Yan^*; Luo, Yong

来源：Journal of Functional Analysis, 2024, 286(3): 110243.

DOI：10.1016/j.jfa.2023.110243

• Bose gases
• Ground states
• Anharmonic traps
• Rotational velocity

This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap V(x) = omega(vertical bar x vertical bar(2)+ k vertical bar x vertical bar(4)) rotating at the velocity Omega > 0, where omega > 0 denotes the trapping frequency, and k > 0 represents the strength of the quartic term. It is known that for any Omega > 0, ground states exist in such traps if and only if 0 < a < a*, where a*:= parallel to Q parallel to(2)(2) and Q > 0 is the unique positive solution of Delta Q - Q + Q(3)= 0 in R-2. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant C > 0, independent of 0 < a < a*, such that ground states do not have any vortex in the region R(a) := {x is an element of R-2 : vertical bar x vertical bar <= C(a* - a)(-1-6 beta 20)} as a NE arrow a*, for the case where omega= 3 Omega(2)/4, k = 1/6, and Omega = C-0(a*- a)(-beta) varies for some beta is an element of[0, 1/6) and C-0 > 0.

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