Localization for random Schrödinger operators with Poisson potential
Stolz, Günter
Annales de l'I.H.P. Physique théorique, Tome 63 (1995), p. 297-314 / Harvested from Numdam
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@article{AIHPA_1995__63_3_297_0,
     author = {Stolz, G\"unter},
     title = {Localization for random Schr\"odinger operators with Poisson potential},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {63},
     year = {1995},
     pages = {297-314},
     mrnumber = {1363537},
     zbl = {0843.60058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1995__63_3_297_0}
}

Stolz, Günter. Localization for random Schrödinger operators with Poisson potential. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 297-314. http://gdmltest.u-ga.fr/item/AIHPA_1995__63_3_297_0/

[1] R. Carmona, One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types, J. Funct. Anal., Vol. 51, 1983, pp. 229-258. | MR 701057 | Zbl 0516.60069

[2] R. Carmonara and J. Lacroix, Spectral theory of random Schrödinger operators, Birkhäuser, Basel-Berlin, 1990. | MR 1102675 | Zbl 0717.60074

[3] E.A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. | MR 69338 | Zbl 0064.33002

[4] J.-M. Combes and P.D. Hislop, Localization for continuous random Hamiltonians in d-dimensions, J. Funct. Anal., Vol. 124, 1994, pp. 149-180. | MR 1284608 | Zbl 0801.60054

[5] R. Del Rio, N. Makarov and B. Simon, Operators with singular continuous spectrum, II. Rank one operators, Commun. Math. Phys., Vol. 165, 1994, pp. 59-67. | MR 1298942 | Zbl 1055.47500

[6] R. Del Rio, B. Simon and G. Stolz, Stability of spectral types for Sturm-Liouville operators, Math. Research Lett., Vol. 1, 1994, pp. 437-450. | MR 1302387 | Zbl 0838.34090

[7] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. | MR 58896 | Zbl 0053.26802

[8] A. Gordon, Pure point spectrum under 1-parameter perturbations and instability of Anderson localization, Commun. Math. Phys., Vol. 164, 1994, pp. 489-506. | MR 1291242 | Zbl 0839.47002

[9] Ph. Hartman, The number of L2-solutions of x'' + q (t) x = 0, Amer. J. Math., Vol. 73, 1951, pp. 635-645. | MR 44695 | Zbl 0044.31202

[10] I.W. Herbst, J.S. Howland, The Stark ladder and other one-dimensional extemal field problems, Commun. Math. Phys., Vol. 80, 1981, pp. 23-42. | MR 623150 | Zbl 0473.47037

[11] P.D. Hilsop, S. Nkamura, Stark Hamiltonians with unbounded random potentials, Rev. Math. Phys., Vol. 2, 1990, pp. 479-494. | MR 1107687 | Zbl 0727.34076

[12] O. Kallenberg, Random Measures, Akademie-Verlag, Berlin, 1975. | MR 431372 | Zbl 0345.60031

[13] J.F.C. Kingman, Poisson Processes, Clarendon Press, Oxford, 1993. | MR 1207584 | Zbl 0771.60001

[14] W. Kirsch, S. Kotani and B. Simon, Absence of absolutely continuous spectrum for some one dimensional random but deterministic potentials, Ann. Inst. Henri Poincaré, Vol. 42, 1985, pp. 383-406. | Numdam | MR 801236 | Zbl 0581.60052

[15] W. Kirsch, S.A. Molchanov and L.A. Pastur, One-dimensional Schrödinger operator with unbounded potential: The pure point spectrum, Funct. Anal. Appl., Vol. 24, 1990, pp. 176-186. | MR 1082027 | Zbl 0747.47023

[16] W. Kirsch, S.A. Molchanov and L.A. Pastur, One-dimensional Schrödinger operator with high potential barriers, Operator Theory: Advances and Applications, Vol. 57, pp. 163-170, Birkhäuser-Verlag, 1992. | MR 1230898 | Zbl 0883.34078

[17] F. Klopp, Localization for Semiclassical Continuous Random Schrödinger Operators II: the Random Displacement Model, Helv. Phys. Acta, Vol. 66, 1993, pp. 810-841. | MR 1264047 | Zbl 0820.60043

[18] S. Kotani, Lyapunov indices determine absolute contnuous spectra of stationnary one dimensional Schrödinger operators, Proc. Taneguchi Intern. Symp. on Stochastic Analysis, Katata and Kyoto, 1982, pp. 225-247, North Holland, 1983. | MR 780760 | Zbl 0549.60058

[19] S. Kotani, Lyapunov exponents and spectra for one-dimensional Schrödinger operators, Contemp. Math., Vol. 50, 1986, pp. 277-286. | Zbl 0587.60054

[20] S. Kotani and B. Simon, Localization in General One-Dimensional Random Systems, Commun. Math. Phys., Vol. 112, 1987, pp. 103-119. | MR 904140 | Zbl 0637.60080

[21] N. Minami, Exponential and Super-Exponential Localizations for One-Dimensional Schrödinger Operators with Lévy Noise Potentials, Tsukuba J. Math., Vol. 13, 1989, pp. 225-282. | MR 1003604 | Zbl 0694.60058

[22] L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, Springer-Verlag, 1991. | MR 1223779 | Zbl 0752.47002

[23] Th Poerschke, G. Stolz and J. Weidmann, Expansions in Generalized Eigenfunctions of Selfadjoint Operators, Math. Z., Vol. 202, 1989, pp. 397-408. | MR 1017580 | Zbl 0661.47021

[24] B. Simon, Trace ideals and their Applications, Cambridge University Press, Cambridge, 1979. | MR 541149 | Zbl 0423.47001

[25] B. Simon, Schrödinger semigroups, Bull. Am. Math. Soc., Vol. 7, 1982, pp. 447-526. | MR 670130 | Zbl 0524.35002

[26] B. Simon, Localization in General One Dimensional Random Systems, I. Jacobi Matrices, Commun. Math. Phys., Vol. 102, 1985, pp. 327-336. | MR 820578 | Zbl 0604.60062

[27] B. Simon and T. Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math., Vol. 39, 1986, pp. 75-90. | MR 820340 | Zbl 0609.47001

[28] G. Stolz, Note to the paper by P.D. Hilsop and S. Nakamura: Stark Hamiltonian with unbounded random potentials, Rev. Math. Phys., Vol. 5, 1993, pp. 453-456. | MR 1223529 | Zbl 0782.34088

[29] G. Stolz, Spectral theory of Schrödinger operators with potentials of infinite barriers type, Habilitationsschrift, Frankfurt, 1994.

[30] G. Stolz, Localization for the Poisson model, in "Spectral Analysis and Partial Differential Equations", Operator Theory: Advances and Applications, Vol. 78, pp. 375-380, Birkhäuser-Verlag, 1955. | MR 1365351 | Zbl 0841.34089

[31] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lect. Notes in Math., Vol. 1258, Springer/Verlag, 1987. | MR 923320 | Zbl 0647.47052