Localization for random Schrödinger operators with Poisson potential
Annales de l'I.H.P. Physique théorique (1995)
- Volume: 63, Issue: 3, page 297-314
- ISSN: 0246-0211
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topStolz, Günter. "Localization for random Schrödinger operators with Poisson potential." Annales de l'I.H.P. Physique théorique 63.3 (1995): 297-314. <http://eudml.org/doc/76697>.
@article{Stolz1995,
author = {Stolz, Günter},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {random Schrödinger operator; localization; eigenfunction},
language = {eng},
number = {3},
pages = {297-314},
publisher = {Gauthier-Villars},
title = {Localization for random Schrödinger operators with Poisson potential},
url = {http://eudml.org/doc/76697},
volume = {63},
year = {1995},
}
TY - JOUR
AU - Stolz, Günter
TI - Localization for random Schrödinger operators with Poisson potential
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 63
IS - 3
SP - 297
EP - 314
LA - eng
KW - random Schrödinger operator; localization; eigenfunction
UR - http://eudml.org/doc/76697
ER -
References
top- [1] R. Carmona, One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types, J. Funct. Anal., Vol. 51, 1983, pp. 229-258. Zbl0516.60069MR701057
- [2] R. Carmonara and J. Lacroix, Spectral theory of random Schrödinger operators, Birkhäuser, Basel-Berlin, 1990. Zbl0717.60074MR1102675
- [3] E.A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. Zbl0064.33002MR69338
- [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. Zbl0801.60054MR1284608
- [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. Zbl1055.47500MR1298942
- [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. Zbl0838.34090MR1302387
- [7] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. Zbl0053.26802MR58896
- [8] A. Gordon, Pure point spectrum under 1-parameter perturbations and instability of Anderson localization, Commun. Math. Phys., Vol. 164, 1994, pp. 489-506. Zbl0839.47002MR1291242
- [9] Ph. Hartman, The number of L2-solutions of x'' + q (t) x = 0, Amer. J. Math., Vol. 73, 1951, pp. 635-645. Zbl0044.31202MR44695
- [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. Zbl0473.47037MR623150
- [11] P.D. Hilsop, S. Nkamura, Stark Hamiltonians with unbounded random potentials, Rev. Math. Phys., Vol. 2, 1990, pp. 479-494. Zbl0727.34076MR1107687
- [12] O. Kallenberg, Random Measures, Akademie-Verlag, Berlin, 1975. Zbl0345.60031MR431372
- [13] J.F.C. Kingman, Poisson Processes, Clarendon Press, Oxford, 1993. Zbl0771.60001MR1207584
- [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. Zbl0581.60052MR801236
- [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. Zbl0747.47023MR1082027
- [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. Zbl0883.34078MR1230898
- [17] F. Klopp, Localization for Semiclassical Continuous Random Schrödinger Operators II: the Random Displacement Model, Helv. Phys. Acta, Vol. 66, 1993, pp. 810-841. Zbl0820.60043MR1264047
- [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. Zbl0549.60058MR780760
- [19] S. Kotani, Lyapunov exponents and spectra for one-dimensional Schrödinger operators, Contemp. Math., Vol. 50, 1986, pp. 277-286. Zbl0587.60054
- [20] S. Kotani and B. Simon, Localization in General One-Dimensional Random Systems, Commun. Math. Phys., Vol. 112, 1987, pp. 103-119. Zbl0637.60080MR904140
- [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. Zbl0694.60058MR1003604
- [22] L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, Springer-Verlag, 1991. Zbl0752.47002MR1223779
- [23] Th Poerschke, G. Stolz and J. Weidmann, Expansions in Generalized Eigenfunctions of Selfadjoint Operators, Math. Z., Vol. 202, 1989, pp. 397-408. Zbl0661.47021MR1017580
- [24] B. Simon, Trace ideals and their Applications, Cambridge University Press, Cambridge, 1979. Zbl0423.47001MR541149
- [25] B. Simon, Schrödinger semigroups, Bull. Am. Math. Soc., Vol. 7, 1982, pp. 447-526. Zbl0524.35002MR670130
- [26] B. Simon, Localization in General One Dimensional Random Systems, I. Jacobi Matrices, Commun. Math. Phys., Vol. 102, 1985, pp. 327-336. Zbl0604.60062MR820578
- [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. Zbl0609.47001MR820340
- [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. Zbl0782.34088MR1223529
- [29] G. Stolz, Spectral theory of Schrödinger operators with potentials of infinite barriers type, Habilitationsschrift, Frankfurt, 1994. Zbl0819.34049
- [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. Zbl0841.34089MR1365351
- [31] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lect. Notes in Math., Vol. 1258, Springer/Verlag, 1987. Zbl0647.47052MR923320
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