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IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 41 (2008) 022002 (12pp) doi:10.1088/1751-8113/41/2/022002
 

Summary: IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL
J. Phys. A: Math. Theor. 41 (2008) 022002 (12pp) doi:10.1088/1751-8113/41/2/022002
FAST TRACK COMMUNICATION
The spectrum of large powers of the Laplacian in
bounded domains
E Katzav and M Adda-Bedia
Laboratoire de Physique Statistique de l'Ecole Normale Sup´erieure, CNRS UMR 8550,
24 rue Lhomond, 75231 Paris Cedex 05, France
E-mail: eytan.katzav@lps.ens.fr and adda@lps.ens.fr
Received 9 October 2007
Published 19 December 2007
Online at stacks.iop.org/JPhysA/41/022002
Abstract
We present exact results for the spectrum of the Nth power of the Laplacian in
a bounded domain. We begin with the one-dimensional case and show that the
whole spectrum can be obtained in the limit of large N. We also show that it is
a useful numerical approach valid for any N. Finally, we discuss implications
of this work and present its possible extensions for non-integer N and for 3D
Laplacian problems.
PACS numbers: 02.60.Lj, 02.30.Tb

  

Source: Adda-Bedia, Mokhtar - Laboratoire de Physique Statistique, Département de Physique, École Normale Supérieure

 

Collections: Physics