Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder

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Abstract

Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper, we study a perturbation problem for embedded eigenvalues for a magnetic Schrödinger operator, when the underlying domain is a cylinder. The magnetic potential is C2 with an algebraic decay rate as the unbounded variable of the cylinder tends to ±∞. In particular, no analyticity of the magnetic potential is assumed. We also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer, thus avoiding the thresholds of the continuous spectrum of the unperturbed operator. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • Imperial College London
  • Saint Petersburg State University
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Fysik
Originalspråkengelska
Artikelnummer012105
TidskriftJournal of Mathematical Physics
Volym58
Utgivningsnummer1
StatusPublished - 2017 jan 1
PublikationskategoriForskning
Peer review utfördJa