The Longuet-Higgins Phase and Charge Transport in Molecular Rings

The Longuet-Higgins-Berry's phase has remarkable consequences for charge transport in molecular rings. For generic (conical) crossing, where the phase is $\pi$, a vanishing cause can lead to a diverging response in the amount of charge transport. Away from level crossings, when the phase is 0, a vanishing cause leads to a vanishing response. The divergence of the response near crossing is related to, but distinct from, the divergence that occurs in the generalized susceptibility. We illustrate this behavior for quantum models of molecular rings driven by a running wave of small amplitude at zero and finite temperatures.