Abstract: We show the emergence of surface Non-Hermitian boundary terms that appear in an extended form of the quantum Ehrenfest theorem and are crucial in the calculation of optical matrix elements that govern the Optical Transitions in semiconductors, e.g. solar cells. Their inevitable existence, strongly related to the boundary conditions of a given quantum mechanical problem, is far-reaching in the sense that they play a dramatic role in the dynamics of solar absorption and the corresponding optical transitions that follow. Processes like optical transitions in localized and delocalized states and probabilities of intermolecular transitions can be investigated through this generalized off-diagonal Ehrenfest theorem, employed in the present work in the form of various physical examples. As a byproduct, an explicit demonstration of bulk-boundary correspondence is shown, as the extended Ehrenfest theorem can be separated into bulk and surface contributions, each behaving separately from the other, but at the end collaborating to give the correct time-derivative of the desired optical element. An additional use is speculated in the case of topological materials.
Keywords: Non-Hermiticity, Ehrenfest Theorem, Optical transitions, solar cells.