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Existence of the Stark-Wannier quantum resonances. (English) Zbl 1303.81079

Summary: In this paper, we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrödinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.{
©2014 American Institute of Physics}

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
82D77 Quantum waveguides, quantum wires
82D25 Statistical mechanics of crystals
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