Spectral shift function for perturbed periodic Schrödinger operators. The large-coupling constant limit case

Article type: Research Article

Authors: Dimassi, Mouez^; | Zerzeri, Maher

Affiliations: LAGA (UMR CNRS 7539), Univ. Paris 13, F-93430 Villetaneuse, France. E-mails: {dimassi, zerzeri}@math.univ-paris13.fr

Note: [] Corresponding author. E-mail: dimassi@math.univ-paris13.fr.

Abstract: In the large coupling constant limit, we obtain an asymptotic expansion in powers of μ−1/δ of the derivative of the spectral shift function corresponding to the pair (Pμ=P0+μW(x),P0=−Δx+V(x)), where W(x) is positive, W(x)~w0(x/|x|)|x|−δ near infinity for some δ>n and w0∈C∞(Sn−1;R+). Here Sn−1 is the unite sphere of the space Rn and μ is a large parameter. The potential V is real-valued, smooth and periodic with respect to a lattice Γ in Rn.

Keywords: periodic Schrödinger operator, spectral shift function, asymptotic expansions, limiting absorption theorem

DOI: 10.3233/ASY-2011-1062

Journal: Asymptotic Analysis, vol. 75, no. 3-4, pp. 233-250, 2011