Non-Hermitian quantum mechanics and exceptional points in molecular electronics.

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.