Abstract
By slightly restricting the conditions given by Herbst and Howland, we prove the existence of resonances in the Stark effect of disordered systems (and atomic crystals) for large atomic mean distance. In the crystal case the ladders of resonances have the Wannier behavior for small complex field.
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Agler, J., Froese, R.: Existence of Stark ladder resonances. Commun. Math. Phys.100, 161–171 (1985)
Avron, J.: On the spectrum ofp 2+V(x)+εx, withV periodic and ε complex. J. Phys. A: Math. Gen.12, 2393–2398 (1979)
Avron, J.: The lifetime of Wannier ladder states. Ann. Phys.143, 33–53 (1982)
Bentosela, F., Caliceti, E., Grecchi, V., Maioli, M., Sacchetti, A.: Analyticity and asymptotics for the Stark-Wannier states. J. Phys. A: Math. Gen.21, 3321–3331 (1988)
Bentosela, F., Grecchi, V.: Stark-Wannier ladders. Commun. Math. Phys.142, 169–192 (1991)
Buslaev, V.S., Dmitrieva, L.A.: A Bloch electron in an external field. Leningrad Math. J.1, 287–320 (1990)
Combes, J.M., Hislop, P.D.: Stark ladder resonances for small electric fields. Commun. Math. Phys.140, 291–320 (1991)
Herbst, I.: Dilation Analyticity in constant electric field: I. The two body problem. Commun. Math. Phys.64, 279–298 (1979)
Herbst, I., Howland, J.: The Stark ladder and other one-dimensional external electric field problems. Commun. Math. Phys.80, 23–42 (1981)
Hunziker, W.: Notes on asymptotic perturbation theory for Schrödinger eigenvalue problems. Helv. Phys. Acta61, 257–304 (1988)
Kato, T.: Perturbation theory for linear operator. Berlin, Heidelberg, New York: Springer 1976
Kirsch, W., Kotani, S., Simon, B.: Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators. Ann. Inst. Henri Poincarè42, 383–406 (1985)
Markushevich, A.: Teoria de las functiones analiticas. MIR, 1970
Morse, P.M., Feshbach, H.: Methods of theoretical Physics, vol. II. New York: McGraw-Hill 1953
Nenciu, A., Nenciu, G.: Existence of Stark-Wannier resonances for non-periodic onedimensional systems. Phys. Rev. B40, 3622–3624 (1989)
Sigal, I.M.: Sharp exponential bounds on resonances states and width of resonances. Adv. Appl. Math.9, 127–166 (1988)
Whittaker, E.T., Watson, G.N.: A course of modern analysis. Cambridge Univ. Press 1965
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Communicated by B. Simon
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Grecchi, V., Maioli, M. & Sacchetti, A. Stark resonances in disordered systems. Commun.Math. Phys. 146, 231–240 (1992). https://doi.org/10.1007/BF02102626
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DOI: https://doi.org/10.1007/BF02102626