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Weak asymptotics of the spectral shift function. (English) Zbl 1121.81047

Summary: We consider the three-dimensional Schrödinger operator with constant magnetic field of strength \(b > 0\), and with smooth electric potential. The weak asymptotics of the spectral shift function with respect to \(b \nearrow +\infty\) is studied. First, we fix the distance to the Landau levels, then the distance to Landau levels tends to infinity as \(b \nearrow +\infty\). In particular we give explicitly the leading terms in the asymptotics and in some case we obtain full asymptotics expansions.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
47A55 Perturbation theory of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
47F05 General theory of partial differential operators
47N50 Applications of operator theory in the physical sciences
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
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