Trace formulae for Schrödinger operators with singular interactions

Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik

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Abstract

Let Σ⊂ℝd be a C-smooth closed compact hypersurface, which splits the Euclidean space ℝd into two domains Ω±. In this note self-adjoint Schrödinger operators with δ and δ'-interactions supported on Σ are studied. For large enough m∈ℕ the difference of mth powers of resolvents of such a Schrödinger operator and the free Laplacian is known to belong to the trace class. We prove trace formulae, in which the trace of the resolvent power difference in L2(ℝd) is written in terms of Neumann-to-Dirichlet maps on the boundary space L2(Σ).
Original languageEnglish
Title of host publicationFunctional Analysis and Operator Theory for Quantum Physics
Subtitle of host publicationThe Pavel Exner Anniversary Volume
EditorsJaroslav Dittrich, Hynek Kovarik, Ari Laptev
Place of PublicationSwitzerland
Pages129-152
Number of pages24
ISBN (Electronic)9783037196755
DOIs
Publication statusPublished - 31 May 2017

Publication series

NameEMS Series of Congress Reports
PublisherEuropean Mathematical Society
Volume12

Keywords

  • trace formula
  • delta interaction
  • Schroedinger operator
  • singular potential

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