Nonlinear localization in thermalized lattices: application to DNA

Abstract

In the last few years numerous studies have been devoted to intrinsic localized modes in nonlinear lattices because they provide examples of localization without disorder. The properties of “discrete breathers” as exact solutions of these nonlinear lattices are now well understood, but this is not the case for the properties of nonlinear localization and energy relaxation in thermalized lattices. In biological molecules such as DNA, where large amplitude nonlinear motions are essential for function, temporary deviations from energy equipartition could play an important role. After a brief introduction to intrinsic localized modes, we address the following questions: (a) does nonlinear localization survive in the presence of a thermal bath and how can we characterize it? (b) what is the origin of localization and how do discrete breathers contribute to it? (c) can we observe nonlinear localization in an experiment? The last point discusses recent results of an experiment performed on DNA, which suggest that the effects of nonlinear localization in a thermalized system may have already been observed.