Effective field approach for long-range dissolved DNA polymer dynamics

Long-range interatomic interactions between distant parts of a DNA helix are known to be dominant factors in determining longitudinal DNA motions. A local field approach has been developed to account for these long-range forces that both simplifies the numerical complications involved in the previous treatment of these interactions and rationalizes the physics. The method leads to excellent agreement with the experimental value for the speed of longitudinal sound ({}2.0 km/s), where agreement was the chief virtue of the earlier method. A new result of this theory is the prediction of one-dimensional plasmon excitations, analogous to plasmons in higher-dimensional charged systems. This one-dimensional plasmon has an electromagnetic character in contrast to the mostly mechanical nature of the slower compressional sound-wave phonon modes. The dispersion for this plasmon mode is soundlike, having a speed of propagation of some 36.0 km/s. Analysis of the effect of viscous frictional forces shows that the one-dimensional plasmon waves are well-defined resonant states for parameter values where the mechanical phonon modes are strongly overdamped.