Journal article

Publication year: 2004

Pages: 70-76

Journal: European Physical Society Letters

Volume number: 67

Issue number: 1

ISSN: 0295-5075

Open access status: Green

DOI Link: https://doi.org/10.1209/epl/i2003-10271-3

Publisher: IOP Publishing

Abstract: 
We compute the relative localization volumes of the vibrational eigenmodes in two-dimensional systems with a regular body but irregular boundaries tinder 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 tinder Neurnann 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.

Harvard Citation style: Russ, S. and Hlushchuk, Y. (2004) Localized low-frequency Neumann modes in 2d systems with rough boundaries, European Physical Society Letters, 67(1), pp. 70-76. https://doi.org/10.1209/epl/i2003-10271-3

APA Citation style: Russ, S., & Hlushchuk, Y. (2004). Localized low-frequency Neumann modes in 2d systems with rough boundaries. European Physical Society Letters. 67(1), 70-76. https://doi.org/10.1209/epl/i2003-10271-3