Spectral shift function for the Stark operator in the large coupling constant limit

Article type: Research Article

Authors: Pushnitski, A.^; | Sloushch, V.

Affiliations: Department of Mathematics, King's College London, Strand, London WC2R 2LS, U.K. E-mail: [email protected] | Department of Mathematical Physics, Faculty of Physics, St. Petersburg State University, 198504, St. Petersburg, Russia E-mail: [email protected]

Note: [] Corresponding author.

Abstract: Let H be the Stark operator in $\mathbb{R}^{3}$ and let V=V(x) be a non-negative potential which decays at infinity as |x|−l for a sufficiently large l>0. The spectral shift function for the pair of operators H+tV, H is studied in the asymptotic regime t→∞. The leading term of the asymptotics is obtained; the result is in agreement with the phase space volume considerations.

Keywords: Stark operator, spectral shift function, large coupling constant

Journal: Asymptotic Analysis, vol. 51, no. 1, pp. 63-89, 2007