منابع مشابه
Eigenmodes of Isospectral Drums
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...
متن کاملThe 2-transitive Transplantable Isospectral Drums
For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [12]; in the present paper, we investigate pairs of domains in R2 which are isospectral but not congruent. All known such counter examples to M. Kac’s famous question can be constructed by a certain tiling method (“transplantability”) using special linear operator groups which act 2-t...
متن کاملResolving 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...
متن کاملIsospectral Metrics and Potentials on Classical Compact Simple Lie Groups
Given a compact Riemannian manifold (M,g), the eigenvalues of the Laplace operator ∆ form a discrete sequence known as the spectrum of (M,g). (In the case the M has boundary, we stipulate either Dirichlet or Neumann boundary conditions.) We say that two Riemannian manifolds are isospectral if they have the same spectrum. For a fixed manifold M , an isospectral deformation of a metric g0 on M is...
متن کاملThe isospectral fruits of representation theory: quantum graphs and drums
We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns techniques of assembly which are both stated generally and demonstrated. For that purpose, quantum graphs are grist to the mill. We develop the intuition that sta...
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ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2018
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s0219887818500603