Abstract

We consider the construction of exactly solvable models of twisted carbon nanotubes by applying Darboux transformation to the square of the Dirac-like Hamiltonian, describing the low-energy dynamics of charge carriers. It is shown that obtained two pseudo-Schrodinger expressions are intertwined, demonstrating supersymmetry structure. It is proved, that for the considered class of pseudo-scalar external perturbations, the unitary disentanglement of negative/ positive states as within Foldy-Wouthuysen (FW) approach, so by Eriksen or SU(2) methods, can be carried out exactly, thus demonstrating the stability of the Dirac sea. The necessity of introduction of the probability density operator into the theory, while considering the problem in FW representation, is underlined.

中文翻译：

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碳纳米管中的超对称和稳定的狄拉克海

摘要

我们考虑通过对像狄拉克一样的哈密顿量的平方进行Darboux变换来构造扭曲碳纳米管的可解模型，从而描述电荷载流子的低能动力学。结果表明，所获得的两个伪薛定inger表达式相互交织，证明了超对称结构。事实证明，对于所考虑的一类伪标量外部扰动，如Foldy-Wouthuysen（FW）方法中那样，负/正状态的统一解缠结，因此可以通过Eriksen或SU（2）方法精确地进行，因此证明了狄拉克海的稳定。强调了在考虑FW表示中的问题的同时将概率密度算子引入理论的必要性。