The spectrum of large powers of the Laplacian in bounded domains

E Katzav; M Adda-Bedia

doi:10.1088/1751-8113/41/2/022002

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arXiv · 0711.2518

The spectrum of large powers of the Laplacian in bounded domains

E Katzav·M Adda-Bedia

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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.

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cond-mat.stat-mech cond-mat.dis-nn cond-mat.other cond-mat.soft math-ph math.MP nlin.SI

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BibTeX RIS

E Katzav, M Adda-Bedia. 2007-11-15. The spectrum of large powers of the Laplacian in bounded domains. https://doi.org/10.1088/1751-8113/41/2/022002

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