论文标题
在玻色恩斯坦冷凝水的大环中的混乱发作
Chaos onset in large rings of Bose-Einstein condensates
论文作者
论文摘要
我们考虑了弱耦合的玻色网凝结物的大环，分析了它们向混乱动力学的过渡和连贯性丧失。最初，一个环被认为是在本征态中的，即在相应位置填充物和相邻位点之间相等的相位差异的相应配置中。这样的环应表现出循环电流，其值将取决于初始的非零相差。这种电流的外观是沿环的建立连贯性的标志。如果相位差在$π/2 $和$3π/2 $之间，而冷凝水的颗粒间相互作用超过了关键的交互价值$ u_c $，则由于系统由于固有的不稳定而进入混乱的状态，因此应该迅速销毁连贯性。但是，这只是故事的一部分。事实证明，混乱的动力学和导致的平均圆电流至零通常被关键的时间尺度$ t_c $所抵消，该级$ t_c $几乎比线性稳定性分析预期的一个数量级要大两个。我们在广泛的参数范围内详细研究了关键的时间尺度。
We consider large rings of weakly-coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e. in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, non-zero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between $π/2$ and $3π/2$ and interparticle interaction in condensates exceeds a critical interaction value $u_c$, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only a part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero is generally offset by a critical time-scale $t_c$, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical time-scale in detail in a broad parameter range.
