Periodic quantum graphs with predefined spectral gaps
Periodic quantum graphs with predefined spectral gaps
Abstract Let Γ be an arbitrary <?CDATA ${\mathbb{Z}}^{n}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:math> -periodic metric graph, which does not coincide with a line. We consider the Hamiltonian <?CDATA ${\mathcal{H}}_{\varepsilon }$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ε</mml:mi> …