Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs Academic Article uri icon

abstract

  • The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics and other areas. A Schnol-type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an sub-exponential growth integral estimate is available. A theorem on spectral gap opening for 'decorated' quantum graphs is established (its analogue is known for the combinatorial case). It is also shown that if a periodic combinatorial or quantum graph has a point spectrum, it is generated by compactly supported eigenfunctions ('scars'). 2005 IOP Publishing Ltd.

published proceedings

  • Journal of Physics A: Mathematical and General

author list (cited authors)

  • Kuchment, P.

citation count

  • 183

complete list of authors

  • Kuchment, Peter

publication date

  • June 2005