Geodesic
On the nature of the Stark--Wannier spectrum
Algebra i analiz, Tome 16 (2004) no. 3, pp. 171-200.

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A. A. Pozharskii. On the nature of the Stark--Wannier spectrum. Algebra i analiz, Tome 16 (2004) no. 3, pp. 171-200. http://geodesic.mathdoc.fr/item/AA_2004_16_3_a5/

[AGZ] Avron J., Gunter L., Zak J., “Energy uncertainty in “Stark ladder””, Solid State Comm., 16:2 (1975), 189–191 | DOI

[AZ] Avron J., Zak J., “Instability of the continuous spectrum: the $N$-band Stark ladder”, J. Math. Phys., 18:5 (1977), 918–921 | DOI | MR

[B1] Buslaev V. S., “Kronig–Penney electron in a homogeneous electric field”, Differential Operators and Spectral Theory, Amer. Math. Soc. Transl. (2), 189, Amer. Math. Soc., Providence, RI, 1999, 45–57 | MR | Zbl

[DK] Deift P., Killip R., “On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials”, Comm. Math. Phys., 203:2 (1999), 341–347 | DOI | MR | Zbl

[DSS] Delyon F., Simon B., Souillard B., “From power pure point to continuous spectrum in disordered systems”, Ann. Inst. H. Poincaré Phys. Théor., 42:3 (1985), 283–309 | MR | Zbl

[E] Exner P., “The absence of the absolutely continuous spectrum for delta' Wannier–Stark ladders”, J. Math. Phys., 36:9 (1995), 4561–4570 | DOI | MR | Zbl

[GP] Gilbert D. J., Pearson D. B., “On subordinacy and analysis of the spectrum of onedimensional Schrödinger operators”, J. Math. Anal. Appl., 128:1 (1987), 30–56 | DOI | MR | Zbl

[K] Kato T., Perturbation theory for linear operators, Springer-Verlag, Berlin, 1995 | MR

[LS] Last Y., Simon B., “Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators”, Invent. Math., 135:2 (1999), 329–367 | DOI | MR | Zbl

[NN] Nenciu A., Nenciu G., “Dynamics of Bloch electrons in external electric fields. I. Bounds for interband transitions and effective Wannier Hamiltonians”, J. Phys. A, 14:10 (1981), 2817–2827 | DOI | MR

[BS] Birman M. Sh., Solomyak M. Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, LGU, L., 1980 | MR

[В2] Buslaev V. S., “Adiabaticheskoe vozmuschenie periodicheskogo potentsiala”, Teor. i mat. fiz., 58:2 (1984), 233–243 | MR | Zbl

[Ва] Buslaeva M. V., “Odnomernyi operator Shredingera s uskoryayuschim potentsialom”, Funkts. anal. i ego pril., 18:1 (1984), 65–66 | MR | Zbl

[BD1] Buslaev V. S., Dmitrieva L. A., “Adiabaticheskoe vozmuschenie periodicheskogo potentsiala. 2”, Teor. i mat. fiz., 73:3 (1987), 430–442 | MR | Zbl

[BD2] Buslaev V. S., Dmitrieva L. A., “Elokhovskii elektron vo vneshnem pole”, Algebra i analiz, 1:2 (1989), 1–29 | MR | Zbl

[BF] Buslaev V. S., Faddeev L. D., “O formulakh sledov dlya differentsialnogo singulyarnogo operatora Shturma–Liuvillya”, Dokl. AN SSSR, 132:1 (1960), 13–16 | MR | Zbl

[Z] Zigmund A., Trigonometricheskie ryady, Mir, M., 1965 | MR

[L] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[Р] Pozharskii A. A., “Ob operatorakh tipa Vane–Shtarka s singulyarnymi potentsialami”, Algebra i analiz, 14:1 (2002), 158–193 | MR | Zbl