Abstract We consider quantum bosons with contact interactions at the Lowest Landau Level (LLL) of a two-dimensional isotropic harmonic trap. At linear order in the coupling parameter g, we construct a large, explicit family of quantum states with energies of the form E 0 + g E 1 / 4 + O ( g 2 ) , where E 0 and E 1 are integers. Any superposition of these states evolves periodically with a period of 8 π / g until, at much longer time scales of order 1 / g 2 , corrections to the energies of order g 2 may become relevant. These quantum states provide a counterpart to the known time-periodic behaviors of the corresponding classical (mean field) theory.

中文翻译：

---

谐波陷阱中弱相互作用玻色子的时间周期量子态

摘要 我们考虑在二维各向同性谐波陷阱的最低朗道能级 (LLL) 处具有接触相互作用的量子玻色子。在耦合参数 g 的线性顺序下，我们构造了一个大的、明确的量子态族，其能量形式为 E 0 + g E 1 / 4 + O ( g 2 ) ，其中 E 0 和 E 1 是整数。这些状态的任何叠加都会以 8 π / g 的周期周期性地演化，直到在 1 / g 2 阶的更长时间尺度上，对 g 2 阶能量的修正可能变得相关。这些量子态提供了对应经典（平均场）理论的已知时间周期行为的对应物。