Localization of low-frequency oscillations in single-walled carbon nanotubes

In the framework of the continuum shell theory, we analytically predict a new phenomenon: the weak localization of optical low-frequency oscillations in carbon nanotubes. We clarify the origin of the localization by means of the concept of the limiting phase trajectory and confirm the obtained analytical results by molecular dynamics simulations of simply supported carbon nanotubes. The performed analysis contributes to the new universal approach to the treatment of nonstationary resonant processes.