Resolving isospectral ‘drums’ by counting nodal domains
نویسندگان
چکیده
منابع مشابه
Resolving isospectral ‘drums’ by counting nodal domains
Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace–Beltrami operators for pairs of flat tori in R with n 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by...
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Recently it was proved that there exist nonisometric planar regions that have identical Laplace spectra. That is, one cannot “hear the shape of a drum.” The simplest isospectral regions known are bounded by polygons with reentrant corners. While the isospectrality can be proven mathematically, analytical techniques are unable to produce the eigenvalues themselves. Furthermore, standard numerica...
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We consider the nodal domains of Gaussian random waves in two dimensions. We present a method to calculate the distribution of the number of nodal domains and the average connectivity with the help of auxiliary Potts-spins. An analytical approach could be helpful to decide whether the pattern of nodal domains belongs to the universality class of short-ranged percolation. This is not completely ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2005
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/38/41/006