  We study the influence of a linear energy bias on a non-equilibrium
excitation on a chain of molecules coupled to local phonons (a tilted Holstein
model) using both a random-walk rate kernel theory and a nonperturbative,
massively parallelized adaptive-basis algorithm. We uncover structured and
discrete vibronic resonance behavior fundamentally different from both linear
response theory and homogeneous polaron dynamics. Remarkably, resonance between
the phonon energy $\hbar\omega$ and the bias $\delta_\epsilon$ occurs not only
at integer but also fractional ratios $\delta_\epsilon/(\hbar\omega) =
\frac{m}{n}$, which effect long-range $n$-bond $m$-phonon tunneling. These
observations are also reproduced in a model calculation of a recently
demonstrated Cy3 system. Potential applications range from molecular
electronics to optical lattices and artificial light harvesting via vibronic
engineering of coherent quantum transport.
