论文标题
谐波陷阱中弱相互作用玻色子的时间周期性量子状态
Time-periodic quantum states of weakly interacting bosons in a harmonic trap
论文作者
论文摘要
我们考虑在二维各向同性谐波陷阱中具有弱接触相互作用的相同量子玻色子，并专注于最低兰道水平（LLL）的状态。按照耦合参数$ g $的线性顺序，我们利用了问题的丰富代数结构，以明确构造一个大型量子状态，其能量$ e_0+e_1+ge_1/4+o（g^2）$，$ e_0 $和$ e_0 $ and $ e_1 $是全部的。结果，这些状态的任何叠加都以最多的$8π/g $定期发展，直到在更长的时间尺度上，订单$ 1/g^2 $，对订单$ g^2 $的校正变得很重要，并可能会破坏这种完全周期性的行为。我们进一步构建了这些状态的类似连贯的组合，它们自然地与适当的制度中的经典动力学联系在一起，并解释了我们的发现如何与相应弱非线性经典理论的已知时间周期特征相关联。我们简要评论了我们分析对其他空间维度和其他类似物理系统的可能概括。
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap, and focus on states at the Lowest Landau Level (LLL). At linear order in the coupling parameter $g$, we exploit the rich algebraic structure of the problem to give an explicit construction of a large family of quantum states with energies of the form $E_0+gE_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. As a result, any superposition of these states evolves periodically with a period of at most $8π/g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ become important and may upset this perfectly periodic behavior. We further construct coherent-like combinations of these states that naturally connect to classical dynamics in an appropriate regime, and explain how our findings relate to the known time-periodic features of the corresponding weakly nonlinear classical theory. We briefly comment on possible generalizations of our analysis to other numbers of spatial dimensions and other analogous physical systems.
