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A Unified Approach for Quantum Chaos and Macroscopic Quantum Dynamics

量子混沌和宏观量子动力学的统一方法

基本信息

批准号：
16540347
负责人：
NAKAMURA Katsuhiro
金额：
$ 2.3万
依托单位：
Osaka City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

Bose-Einstein condensate(BEC) provides a nice stage when the nonlinear Schr{"o}dinger equation plays a vital role.We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinearSchr{"o}dinger (or Gross-Pitaevskii) equation.Firstly we consider a driven two-component BEC with each component trapped in different vertical positions.The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom.The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass.Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules.We obtain an effective nonlinear dynamics for three vortex cores,which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance $r_{ij}$ on short scale and logarithmic in $r_{ij}$ on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager.We then explore "the chaos in the three-body problem" in the context of vortices with inertia.

玻色-爱因斯坦凝聚（BEC）为非线性薛定谔方程发挥重要作用提供了一个很好的舞台。利用非线性schr {"o}dinger （Gross-Pitaevskii）方程，研究了含谐波阱的二维多分量排斥BEC的动力学。首先，我们考虑一个驱动的双分量BEC，每个分量被困在不同的垂直位置。适当调整磁场振荡频率，可使BEC具有显著的反重力输运。这种现象是具有两个内（电子）自由度的系统中宏观非绝热隧穿现象的一种表现。动力学分裂为每个凝聚波函数的快速复杂时空振荡以及总质心的缓慢悬浮。其次，我们研究了二维无磁场条件下谐波阱中三分量的排斥性BEC，建立了基于涡旋分子图像的保守混沌模型。我们得到了均匀磁场下三个带电粒子的有效非线性动力学模型，在短尺度下，粒子间斥力势在涡旋间距离$r_{ij}$为二次元，在大尺度上，粒子间斥力势在$r_{ij}$为对数。这里的涡旋获得的惯性与Onsager以来的点涡旋的标准理论有明显的对比。然后，我们在具有惯性的涡旋的背景下探讨“三体问题中的混沌”。