A semiclassical theory developed in a previous paper [K. G. Kay, Phys. Rev. A 96, 042116 (2017)] is applied to calculate tunneling splittings for arbitrary vibrational states of model two-dimensional double-well systems. Cases in which the classical dynamics for the wells is chaotic, mixed, and regular are considered. A perturbative treatment, based on the condition of small tunneling amplitudes, is found to be sufficiently accurate for the cases studied and is applied for most of the calculations. Treatments that approximate certain imaginary-time trajectories in the classically forbidden region by linearization about a variety of judiciously selected reference trajectories yield good results for all systems treated. These calculations can be greatly simplified by approximating all imaginary-time trajectories as linearizations about a single reference trajectory. A simple way to determine optimal reference trajectories for this purpose is presented. It is found that their use yields splittings of satisfactory accuracy for the cases studied.

中文翻译：

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多维双井中任意振动状态的半经典隧穿裂隙

在先前的论文中提出的半经典理论[KG Kay，Phys。A版96，042116（2017）]用于计算二维二维双井系统任意振动状态的隧穿裂隙。考虑井的经典动力学是混沌，混合和规则的情况。发现基于小隧穿振幅的条件的摄动处理对于所研究的情况是足够准确的，并且被用于大多数计算。通过对各种明智选择的参考轨迹进行线性化处理，可以近似地将经典禁区中的某些虚时轨迹进行处理，从而为所有处理过的系统带来了良好的效果。通过将所有虚拟时间轨迹近似为关于单个参考轨迹的线性化，可以大大简化这些计算。为此，介绍了一种确定最佳参考轨迹的简单方法。发现在所研究的情况下，它们的使用产生令人满意的精度的分裂。