Bloch-like oscillations in the Peyrard-Bishop-Holstein model

The Peyrard-Bishop-Holstein model has been previously introduced as an appropriate framework for the description of polaronic effects for charge migration in DNA. We study numerically the Peyrard-Bishop-Holstein model when the charge carrier is also subjected to an applied uniform electric field. We find that the polaron undergoes coherent oscillations when the electric field is applied along the stacking direction. The frequency of the oscillations is the same as in the rigid lattice (Bloch frequency) provided that the carrier-lattice coupling is not large. Increasing the coupling the single peak of the Fourier spectrum splits into side peaks around the Bloch frequency