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Abstract
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In the semiclassical regime (i.e.,
),
we study the effect of a slowly varying potential
on the magnetic
Schrödinger operator
on a strip
.
The potential
is assumed to be smooth. We derive the semiclassical dynamics and we describe the
asymptotic structure of the spectrum and the resonances of the operator
for
small enough. All our results depend on the eigenvalues corresponding to
on
with
Dirichlet boundary condition.
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Keywords
semiclassical analysis, periodic Schrödinger operator,
Bohr–Sommerfeld quantization, spectral shift function,
asymptotic expansions, limiting absorption theorem
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Mathematical Subject Classification 2010
Primary: 35P20, 47A55, 47N50, 81Q10, 81Q15
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Milestones
Received: 10 October 2018
Revised: 17 November 2018
Accepted: 2 December 2018
Published: 22 March 2019
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