×

Stark resonances in disordered systems. (English) Zbl 0770.47030

By slightly restricting the conditions given by I. W. Herbst and J. S. Howland [Commun. Math. Phys. 80, 23-42 (1981; Zbl 0473.47037)], 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.

MSC:

47N50 Applications of operator theory in the physical sciences
81V10 Electromagnetic interaction; quantum electrodynamics
81T10 Model quantum field theories

Citations:

Zbl 0473.47037
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agler, J., Froese, R.: Existence of Stark ladder resonances. Commun. Math. Phys.100, 161–171 (1985) · Zbl 0651.47006
[2] Avron, J.: On the spectrum ofp 2+V(x)+{\(\epsilon\)}x, withV periodic and {\(\epsilon\)} complex. J. Phys. A: Math. Gen.12, 2393–2398 (1979) · Zbl 0447.34024
[3] Avron, J.: The lifetime of Wannier ladder states. Ann. Phys.143, 33–53 (1982)
[4] 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) · Zbl 0655.46059
[5] Bentosela, F., Grecchi, V.: Stark-Wannier ladders. Commun. Math. Phys.142, 169–192 (1991) · Zbl 0743.35053
[6] Buslaev, V.S., Dmitrieva, L.A.: A Bloch electron in an external field. Leningrad Math. J.1, 287–320 (1990) · Zbl 0726.34070
[7] Combes, J.M., Hislop, P.D.: Stark ladder resonances for small electric fields. Commun. Math. Phys.140, 291–320 (1991) · Zbl 0737.34060
[8] Herbst, I.: Dilation Analyticity in constant electric field: I. The two body problem. Commun. Math. Phys.64, 279–298 (1979) · Zbl 0447.47028
[9] Herbst, I., Howland, J.: The Stark ladder and other one-dimensional external electric field problems. Commun. Math. Phys.80, 23–42 (1981) · Zbl 0473.47037
[10] Hunziker, W.: Notes on asymptotic perturbation theory for Schrödinger eigenvalue problems. Helv. Phys. Acta61, 257–304 (1988)
[11] Kato, T.: Perturbation theory for linear operator. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0342.47009
[12] 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) · Zbl 0581.60052
[13] Markushevich, A.: Teoria de las functiones analiticas. MIR, 1970
[14] Morse, P.M., Feshbach, H.: Methods of theoretical Physics, vol. II. New York: McGraw-Hill 1953 · Zbl 0051.40603
[15] Nenciu, A., Nenciu, G.: Existence of Stark-Wannier resonances for non-periodic onedimensional systems. Phys. Rev. B40, 3622–3624 (1989)
[16] Sigal, I.M.: Sharp exponential bounds on resonances states and width of resonances. Adv. Appl. Math.9, 127–166 (1988) · Zbl 0652.47008
[17] Whittaker, E.T., Watson, G.N.: A course of modern analysis. Cambridge Univ. Press 1965 · JFM 45.0433.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.