Polaron normal modes in the Peyrard-Bishop-Holstein model

A number of experimental and theoretical works have suggested the relevance of polaronic effects for charge migration in DNA. We have previously introduced the Peyrard-Bishop-Holstein model as an appropriate model for the description of such effects. The polaron normal modes are expected to manifest themselves through the response of the system in an external time-periodic field. Here, following a brief presentation of the polaron solutions and their energies in the Peyrard-Bishop-Holstein model, we report the normal modes of these solutions and discuss the complete density of states of polaron eigenfrequencies and its dependence on the charge-lattice coupling constant. We find a rather intriguing behavior of some localized modes, integral to the polaron, as they show level crossings and avoided level crossings, and/or change character from being predominantly lattice (or electronic) modes for strong charge-lattice coupling to becoming almost exclusively electronic (phononic) modes as the coupling decreases.