Localized low-frequency Neumann modes in 2d systems with rough boundariesS. Russ and Y. Hlushchuk
Institut für Theoretische Physik III, Universität Giessen - D-35392 Giessen, Germany
(Received 15 December 2003; accepted in final form 26 April 2004)
We compute the relative localization volumes of the vibrational eigenmodes in two-dimensional systems with a regular body but irregular boundaries under Dirichlet and under Neumann boundary conditions. We find that localized states are rare under Dirichlet boundary conditions but very common in the Neumann case. In order to explain this difference, we utilize the fact that under Neumann conditions the integral of the amplitudes carried out over the whole system area is zero. We discuss how this condition leads to many localized states in the low-frequency regime and show, by numerical simulations, how the number of the localized states and their localization volumes vary with the boundary roughness.
71.23.An - Theories and models; localized states.
63.20.Pw - Localized modes.
72.15.Rn - Localization effects (Anderson or weak localization).
© EDP Sciences 2004