On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Abstract

We study the following nonlocal mixed order Gross-Pitaevskii equation $$i{\partial }_t\psi =-\frac{1}{2}\Delta \psi +V_{ext}\psi +{\lambda }_1|\psi {|}^2\psi +{\lambda }_2(K\ast |\psi {|}^2)\psi +{\lambda }_3|\psi {|}^{p-2}\psi ,$$ where $K$ is the classical dipole-dipole interaction kernel, ${\lambda }_3>0$ and $p\in (4,6]$; the case $p=6$ being energy critical. For $p=5$ the equation is considered currently as the state-of-the-art model for describing the dynamics of dipolar Bose-Einstein condensates (Lee-Huang-Yang corrected dipolar GPE). We prove existence and nonexistence of standing waves in different parameter regimes; for $p\ne 6$ we prove global well-posedness and small data scattering.

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Cited by in corpus (2)

• Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction
• Ground states for a nonlocal cubic-quartic Gross-Pitaevskii equation