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.

Figure 1

Carrier wave function (upper panel) and lattice displacement (lower panel) at $t=0$ for different values of $\chi$ and $N=500$.

Figure 2

(Color online) (a) Carrier wave function and (b) lattice displacement as a function of position and time in a lattice of $N=1000$ sites for $\chi =0.1\text{eV}/\text{Å}$ and $F=3.0\text{mV}/\text{Å}$ showing their oscillatory behavior.

Figure 3

(a) Centroid of the carrier wave function and (b) $l\left(t\right)$ as a function of time in a lattice of $N=1000$ sites for $\chi =0.1\text{eV}/\text{Å}$ and $F=3.0\text{mV}/\text{Å}$. The insets show the corresponding Fourier transform.

Figure 4

Current density as a function of time when $F=10\text{mV}/\text{Å}$ for different values of the coupling constant, namely, $\chi =0.1,0.2,0.3\text{eV}/\text{Å}$ from top to bottom. The left panels show the oscillatory behavior over a short-time interval. The right panels only show the envelope of the current and over a much longer time interval.

Figure 5

Fourier transform of the current density $J\left(t\right)$ for $F=10\text{mV}/\text{Å}$ (left panels) and $F=30\text{mV}/\text{Å}$ (right panels) and three different values of the coupling constant, namely, $\chi =0.1,0.2,0.3\text{eV}/\text{Å}$ from top to bottom.