We consider the simplest nonintegrable model of the multistate Landau-Zener transition. In this model, two pairs of levels in two tunnel-coupled quantum dots are swept past each other by the gate voltage. Although this $2\times 2$ model is nonintegrable, it can be solved analytically in the limit when the interlevel energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar $2\times 1$ model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In the $2\times 1$ model, the probability for a particle, residing at time $t\to -\infty$ in one dot, to remain in the same dot at $t\to \infty$, falls off exponentially with tunnel coupling. By contrast, in the $2\times 2$ model, this probability grows rapidly with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as a manifestation of the Dicke effect.

中文翻译：

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在不可积分的多州Landau-Zener模型中，绝热性随着隧穿间隙的增加而损失

我们考虑了多州Landau-Zener过渡的最简单的不可积模型。在该模型中，两个隧道耦合量子点中的两对能级被栅极电压扫过。虽然这个$\mathrm{2个}\times \mathrm{2个}$该模型是不可积分的，当层间能量距离远小于其隧道裂隙时，可以在极限条件下求解。结果与类似的对比$\mathrm{2个}\times \mathrm{1个}$模型，其中一个点仅包含一个级别。后一种模型不允许虚拟过渡幅度的干扰，并且可以完全解决。在里面$\mathrm{2个}\times \mathrm{1个}$ 模型，存在于某个时间的粒子的概率 $Ť\to -\infty$ 在一个点上，以保持在同一点上 $Ť\to \infty$，与隧道耦合呈指数下降。相比之下，在$\mathrm{2个}\times \mathrm{2个}$在模型中，这种概率随着隧道耦合而迅速增长。这种增长的物理原因是在两个点的系统中隧道效应引起的集体态的形成。这可以看作是迪克效应的体现。