Dispersion relations of periodic quantum graphs associated with Archimedean tilings. II. (English) Zbl 1509.81598
Summary: We continue the work of a previous paper [Y.-C. Luo et al., J. Phys. A, Math. Theor. 52, No. 16, Article ID 165201, 22 p. (2019; Zbl 1509.81597)] to derive the dispersion relations of the periodic quantum graphs associated with the remaining 5 of the 11 Archimedean tilings, namely the truncated hexagonal tiling \((3, 12^2)\), rhombi-trihexagonal tiling \((3, 4, 6, 4)\), snub square tiling \((3^2, 4, 3, 6)\), snub trihexagonal tiling \((3^4, 6)\), and truncated trihexagonal tiling \((4, 6, 12)\). The computation is done with the help of the symbolic software Mathematica. With these explicit dispersion relations, we perform more analysis on the spectra.
MSC:
| 81U30 | Dispersion theory, dispersion relations arising in quantum theory |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 05B45 | Combinatorial aspects of tessellation and tiling problems |
Keywords:
characteristic functions; Floquet-Bloch theory; uniform tiling; absolutely continuous spectrumCitations:
Zbl 1509.81597References:
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