Fractional Laplacian in bounded domains.
The fractional Laplacian operator -(-delta)(alpha/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 eigenvalue spectrum are also obtained.
Zoia
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Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. andrea.zoia@polimi.it
Rosso
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Kardar
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