Let H-B be any fixed one-dimensional Bloch Hamiltonian with only the first m gaps open and H-F = H-B + Fx be the corresponding Stark Hamiltonian. For any positive F small enough H-F has only m ladders of sharp resonances given by the analytic translation method, the decoupled band approximation and the regular perturbation theory. This way, the Wannier conjecture becomes a definite regular perturbation theory for the Stark ladders as eigenvalues of the translated Hamiltonian.
STARK LADDERS OF RESONANCES - WANNIER LADDERS AND PERTURBATION-THEORY / V., Grecchi; Maioli, Marco; Sacchetti, Andrea. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 159:(1994), pp. 605-618.
STARK LADDERS OF RESONANCES - WANNIER LADDERS AND PERTURBATION-THEORY
MAIOLI, Marco;SACCHETTI, Andrea
1994
Abstract
Let H-B be any fixed one-dimensional Bloch Hamiltonian with only the first m gaps open and H-F = H-B + Fx be the corresponding Stark Hamiltonian. For any positive F small enough H-F has only m ladders of sharp resonances given by the analytic translation method, the decoupled band approximation and the regular perturbation theory. This way, the Wannier conjecture becomes a definite regular perturbation theory for the Stark ladders as eigenvalues of the translated Hamiltonian.
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