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On the third critical speed for rotating Bose-Einstein condensates. (English) Zbl 1344.81175
The present paper studies a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap within the framework of the Gross-Pitaevskii theory. In the Thomas-Fermi regime, there have already been a number of papers devoted to this topic in the literature, which identified three phase transitions corresponding to three critical values of the rotational velocity (denoted by \(\Omega\)) of the anharmonic trap. The target of the present paper is the giant vortex state, which emerges at the rapid rotation regime when the third critical rotation speed is crossed. The main result that the authors obtained in the present paper is an estimate of this critical speed. They found that the condensate is in the giant vortex phase if \(\Omega=\Omega_0/\varepsilon^4\) with \(\Omega_0>\Omega_c\), where \(\Omega_c\) is a finite value. The authors also conjectured that the critical point lies precisely at \(\Omega=\Omega_c/\varepsilon^4\), but the proof of this claim is left for future work. Apart from the results on the third critical speed, the authors also proved a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.

MSC:
81V70 Many-body theory; quantum Hall effect
35Q55 NLS equations (nonlinear Schrödinger equations)
76U05 General theory of rotating fluids
76B47 Vortex flows for incompressible inviscid fluids
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
Software:
GPELab
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References:
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