Periodic quantum graphs from the Bethe–Sommerfeld perspective

DOI10.1088/1751-8121/aa8d8dzbMath1383.81090arXiv1705.07306OpenAlexW3100642090MaRDI QIDQ4596386

Pavel Exner, Ondřej Turek

Publication date: 1 December 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.07306

zbMATH Keywords

Diophantine approximationquantum graphsperiodic structurevertex couplingBethe-Sommerfeld conjecture

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Diophantine approximation in probabilistic number theory (11K60) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (12)

Nodal statistics on quantum graphs ⋮ Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover ⋮ Continued fractions with bounded even-order partial quotients ⋮ Gaps in the spectrum of a cuboidal periodic lattice graph ⋮ Degenerate band edges in periodic quantum graphs ⋮ Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set ⋮ Multidimensional almost-periodic Schrödinger operators with Cantor spectrum ⋮ On the eigenvalues of quantum graph Laplacians with large complex \(\delta\) couplings ⋮ One-sided Diophantine approximations ⋮ Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip ⋮ Mass-constrained ground states of the stationary NLSE on periodic metric graphs ⋮ Periodic quantum graphs with predefined spectral gaps

Cites Work

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