J. Behrndt, M. Langer and V. Lotoreichik,
Trace formulae for Schrödinger operators with singular interactions,
in "Functional Analysis and Operator Theory for Quantum Physics",
European Math. Soc., Zürich, 2017, pp. 129–152
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).