We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type demonstrate the phenomenon of partial localization of under-barrier states, possibly resulting in the appearance of the so-called “resonant” tunneling, or the phenomenon of coherent tunneling destruction, referring to the complete localization. Taking the partial localization and the coherent tunneling destruction as basic examples, we indicate main advantages of using isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems with two- and three-well potentials. They, in particular, are: having enough freedom of changing the potential shape in a wide range, that allows one to choose an exactly-solvable model close to characteristics of the phenomenological one; ability of changing the number of local minima and symmetry characteristics of the potential (symmetric or deformed) without changing the main part of the spectrum; engaging a smart basis of states, that dramatically decreases the dimensionality of matrices used in the diagonalization procedure of the corresponding spectral problem.

我们研究了具有多孔势和破坏反射对称性的 N=4 超对称量子力学的精确可解模型中隧道动力学的特征。具有这种现象学潜力的量子系统表现出低于势垒状态的部分局域化现象，可能导致所谓的“共振”隧穿现象的出现，或相干隧穿破坏现象，指的是完全局域化。以部分局域化和相干隧穿破坏为基本例子，我们指出了在研究具有二阱和三阱势的量子力学系统时使用等谱精确可解哈密顿量的主要优点。它们尤其是：具有在大范围内改变潜在形状的足够自由，这允许人们选择一个接近于现象学特征的完全可解的模型；在不改变谱的主要部分的情况下改变势的局部最小值和对称特性的数量的能力（对称或变形）；使用状态的智能基础，这大大降低了相应谱问题的对角化过程中使用的矩阵的维数。