In non-Hermitian (NH) quantum mechanics, Hamiltonians are studied whose eigenvalues are not necessarily real since the condition of hermiticity is not imposed. Certain symmetries of NH operators can ensure that some or all of the eigenvalues are real and thus suitable for the description of physical systems whose energies are always real. While the mathematics of NH quantum mechanics is well developed, applications of the theory to real quantum systems are scarce, and no closed system is known whose Hamiltonian is NH. Here, we consider the elementary textbook example of a NH Hamiltonian matrix, and we show how it naturally emerges as a simplifying concept in the modeling of molecular electronic devices. We analyze the consequences of non-Hermiticity and exceptional points in the spectrum of NH operators for the molecular conductance and the spectral density of simple models for molecules on surfaces.

中文翻译：

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非赫米特量子力学和分子电子学中的特长。

在非Hermitian（NH）量子力学中，研究了哈密顿量，其特征值不一定是真实的，因为没有施加遗传性条件。NH算子的某些对称性可以确保某些或所有特征值是真实的，因此适合描述能量始终为真实的物理系统。尽管NH量子力学的数学已经得到很好的发展，但是该理论在实际量子系统中的应用却很少，而且还不知道哈密顿量为NH的封闭系统。在这里，我们考虑NH Hamiltonian矩阵的基本教科书示例，并展示它如何自然地作为简化概念出现在分子电子设备的建模中。