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Magnetic scattering at low energy in two dimensions. (English) Zbl 0934.35140

The author considers the two-dimensional Schrödinger operator with compactly supported magnetic field \(b\) and compactly supported electric potential \(V\). Under the assumption that the total flux of \(b\) is not an integer, it is shown that the resonant space at zero energy has dimension at most two, and an asymptotic formula is obtained for the scattering amplitude when the energy tends to zero. As an application, the behaviour of the scattering amplitude is studied in the case where the magnetic field tends towards a Dirac measure.

MSC:

35Q40 PDEs in connection with quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
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