Periodically driven DNA: Theory and simulation

We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude $F$ and frequency $\nu$ and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, $A_{\rm loop}$, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length $L$ and the system has only one scaling ($A_{\rm loop} \approx \nu^{-1}F^2)$. Expansion of an analytical expression for $A_{\rm loop}$ obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force ($A_{\rm loop} \approx \nu^{-1}F^{2.5}$), which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite $L$, the exponents are robust and independent of temperature and friction coefficient.