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arXiv 2003.03684cond-mat.quant-gashep-thmath-phmath.MPquant-ph
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简谐势阱中弱相互作用玻色子的时间周期量子态

Time-periodic quantum states of weakly interacting bosons in a harmonic trap

Marine De Clerck, Oleg Evnin

备注：
14 pages, v2: published version
发表信息：
Phys. Lett. A 384 (2020) 126930
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摘要：

本文研究了二维各向同性谐振子阱中具有弱接触相互作用的全同玻色子，并着重研究了最低朗道能级（LLL）下的态。在耦合参数$g$的线性阶，我们利用丰富的代数结构的问题，给出一个显式的结构的一个大家庭的量子态的能量的形式$E_0+gE_1/4+O(g^2)$，其中$E_0$和$E_1$是整数。结果，这些态的任何叠加都以至多$8π/g$的周期周期性地演化，直到在更长的$1/g^2$阶时间尺度上，对$g^2$阶能量的校正变得重要，并且可能扰乱这种完美的周期性行为。我们进一步构建了这些状态的相干组合，这些状态在适当的制度中自然地连接到经典动力学，并解释了我们的研究结果如何与相应的弱非线性经典理论的已知时间周期特征相关。我们简要地评论我们的分析可能的推广到其他数量的空间维度和其他类似的物理系统。

英文摘要：

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.

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