Fractional Laplacian in Bounded Domains
| dc.creator | Zoia, A. | |
| dc.creator | Rosso, A. | |
| dc.creator | Kardar, M. | |
| dc.date | 2007-06-08 | |
| dc.date.accessioned | 2026-07-07T08:41:45Z | |
| dc.date.available | 2026-07-07T08:41:45Z | |
| dc.description | The fractional Laplacian operator, $-(-\triangle)^{\fracα{2}}$, appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained. | |
| dc.description | 11 pages, 11 figures | |
| dc.identifier | https://arxiv.org/abs/0706.1254 | |
| dc.identifier | http://arxiv.org/abs/0706.1254 | |
| dc.identifier | PHYSICAL REVIEW E 76, 021116 (2007) | |
| dc.identifier | doi:10.1103/PhysRevE.76.021116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141773 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Fractional Laplacian in Bounded Domains | |
| dc.type | text |