Driben R, Konotop V V, Meier T
Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany.
ITMO University, 49 Kronverskii Ave., St. Petersburg 197101, Russian Federation.
Sci Rep. 2016 Mar 11;6:22758. doi: 10.1038/srep22758.
Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems.
非线性是自然界中众多重要效应的驱动力，这些效应通常表现出不同状态之间的转变，包括规则、混沌或灾难性的行为。局域非线性模式一直是流体和气体动力学、光子学、原子与固态物理等领域深入研究的焦点。由于非线性系统行为的丰富性以及精确三维（3D）数值模拟对数值的严苛要求，目前关于三维复杂非线性模式动力学的了解还很少。在此，我们研究了被困在抛物形势阱中并通过排斥性非线性相互作用的三维非共轴物质波涡旋的动力学。我们的数值模拟表明，存在一种意想不到且引人入胜的非线性状态，当非线性开启时立即出现，其特征是一种平滑的动力学，表现为无扭矩进动并伴有章动。事实证明，所报道的运动在诸如粒子数量、耗散和势阱变形等各种效应方面具有鲁棒性，因此在经过适当设计的实验中应该是可观测的。由于我们的理论方法，即耦合非线性薛定谔方程，具有相当的通用性，我们预计所获得的这种新颖的动力学行为也应该存在于其他非线性系统中。
