The nonexistence of vortices for rotating Bose-Einstein condensates in non-radially symmetric traps

As a continuation of [34], we consider ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps V(x) = x(1)(2)+Lambda(2)x(2)(2), where 0 < Lambda not equal 1and x =( x(1), x(2)) is an element of R-2. For any fixed rotational velocity 0 <= O < Omega < Omega* := 2 min{1,Lambda}, it is known that ground states exist if and only if a < a* for some critical constant 0 < a* 0 denotes the product of the number of particles and the absolute value of the scattering length. We analyze the asymptotic expansions of ground states as a NE arrow a*, which display the visible effect of Omega on ground states. As a consequence, we further prove that ground states do not have any vortex in the region R(a) :={x is an element of R-2 :|x| <= C(a*- a)- 1/12} as a NE arrow a* for some constant C> 0, which is independent of 0 < a < a*. (c) 2022 Elsevier Masson SAS. All rights reserved.

Automated summary

This paper investigates the ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps. The authors analyze the asymptotic expansions of the ground states as the critical constant approaches a certain value, showing the visible effect of the rotational velocity on the ground states. Furthermore, it is proven that the ground states do not have any vortex in a specific region.