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Condensed Matter > Other Condensed Matter
Title: Eigenmodes of the Laplacian on Hyperbolic Lattices
(Submitted on 14 Jun 2023 (v1), last revised 22 Apr 2024 (this version, v3))
Abstract: We examine a specific category of eigenfunctions of the lattice Laplacian on $\{p,q\}$-tessellations of the Poincar\'e disk that bear resemblance to plane waves in the continuum case. Our investigation reveals that the lattice eigenmodes deviate from the continuum solutions by a factor that depends solely on the local inclination of the vertex in relation to the wave's propagation direction. This allows us to compute certain eigenfunctions by numerical and analytical methods. For various special cases we find explicit exact eigenfunctions and their eigenvalues on the infinite lattice.
Submission history
From: Eric Petermann [view email][v1] Wed, 14 Jun 2023 05:29:36 GMT (3218kb,D)
[v2] Wed, 21 Jun 2023 08:04:45 GMT (4144kb,D)
[v3] Mon, 22 Apr 2024 20:18:14 GMT (5566kb,D)
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