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Volumn 8, Issue 11, 1997, Pages 1817-1854

Generalized Floquet theory for stationary Schrödinger operators in one dimension

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBABILITY; RANDOM PROCESSES;

EID: 0031271826     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(97)00042-8     Document Type: Article
Times cited : (54)

References (42)
  • 1
    • 0000423029 scopus 로고
    • The rotation number for almost periodic potentials
    • Johnson, R. and Moser, J., The rotation number for almost periodic potentials. CMP, 1982, 84, 403-438.
    • (1982) CMP , vol.84 , pp. 403-438
    • Johnson, R.1    Moser, J.2
  • 2
    • 24244444170 scopus 로고
    • Absences of diffusion in certain random lattices
    • Anderson, Ph., Absences of diffusion in certain random lattices. Physical Review, 1958, 109, 1492-1505.
    • (1958) Physical Review , vol.109 , pp. 1492-1505
    • Anderson, Ph.1
  • 3
    • 34250283162 scopus 로고
    • A pure point spectrum of the stochastic and one dimensional schrödinger equation
    • Goldsheid, I. Ja., Molchanov, S. A. and Pastusr, L. A., A pure point spectrum of the stochastic and one dimensional Schrödinger equation. Funct. Anal. Appl., 1977, 11, 1-10.
    • (1977) Funct. Anal. Appl. , vol.11 , pp. 1-10
    • Goldsheid, I.Ja.1    Molchanov, S.A.2    Pastusr, L.A.3
  • 4
    • 0001848182 scopus 로고
    • Ljapunov indices determine absolutely continuous spectra of stationary one dimensional Schrödinger operators
    • ed. K. Itô. North-Holland, Kyoto
    • Kotani, S., Ljapunov indices determine absolutely continuous spectra of stationary one dimensional Schrödinger operators. In Proc. Taniguchi Int. Symp. on SA, ed. K. Itô. North-Holland, Kyoto, 1982, pp. 225-247.
    • (1982) Proc. Taniguchi Int. Symp. on SA , pp. 225-247
    • Kotani, S.1
  • 5
    • 0001797129 scopus 로고
    • One-dimensional schrödinger operators and Herglotz functions
    • ed. K. Itô. North-Holland, Kyoto
    • Kotani, S., One-dimensional Schrödinger operators and Herglotz functions. In Proc. Taniguchi Int. Symp. on Stochastic Processes and Math. Phys., ed. K. Itô. North-Holland, Kyoto, 1985, pp. 219-250.
    • (1985) Proc. Taniguchi Int. Symp. on Stochastic Processes and Math. Phys. , pp. 219-250
    • Kotani, S.1
  • 6
    • 84856125861 scopus 로고
    • A characterization of the spectrum of Hill's operator
    • Marchenko, V. A. and Ostrovskii, I. V., A characterization of the spectrum of Hill's operator. Math. USSR Sbornik, 1975, 97, 493-554.
    • (1975) Math. USSR Sbornik , vol.97 , pp. 493-554
    • Marchenko, V.A.1    Ostrovskii, I.V.2
  • 7
    • 0030542572 scopus 로고    scopus 로고
    • Spectra of non-self adjoint Hill's operators and a class of Riemann surfaces
    • Tkachenko, V., Spectra of non-self adjoint Hill's operators and a class of Riemann surfaces. Ann. Math., 1996, 143, 181-231.
    • (1996) Ann. Math. , vol.143 , pp. 181-231
    • Tkachenko, V.1
  • 8
    • 84972546484 scopus 로고
    • Subharmonicity of the Lyaponov index
    • Craig, W. and Simon, B., Subharmonicity of the Lyaponov index. Duke Math. J., 1983, 50, 551-560.
    • (1983) Duke Math. J. , vol.50 , pp. 551-560
    • Craig, W.1    Simon, B.2
  • 9
    • 34250250635 scopus 로고
    • Spectral properties of disordered systems in the one body approximation
    • Pastur, L. A., Spectral properties of disordered systems in the one body approximation. CMP, 1980, 75, 167-196.
    • (1980) CMP , vol.75 , pp. 167-196
    • Pastur, L.A.1
  • 10
    • 0002835770 scopus 로고
    • Localization of eigenstates and transport phenomena in the one-dimensional disordered system
    • Ishii, K., Localization of eigenstates and transport phenomena in the one-dimensional disordered system. Suppl. Progr. Theor. Phys., 1973, 53, 77-138.
    • (1973) Suppl. Progr. Theor. Phys. , vol.53 , pp. 77-138
    • Ishii, K.1
  • 11
    • 0000451964 scopus 로고
    • Kotani theory for one dimensional stochastic Jacobi matrices
    • Simon, B., Kotani theory for one dimensional stochastic Jacobi matrices. CMP, 1983, 89, 227-234.
    • (1983) CMP , vol.89 , pp. 227-234
    • Simon, B.1
  • 12
    • 0000798213 scopus 로고
    • Support theorems for random Schrödinger operators
    • Kotani, S., Support theorems for random Schrödinger operators. CMP, 1985, 97, 443-452.
    • (1985) CMP , vol.97 , pp. 443-452
    • Kotani, S.1
  • 13
    • 0000505933 scopus 로고
    • Absence of absolutely continuous spectrum for some one dimensional random but deterministic potentials
    • Kirsch, W., Kotani, S. and Simon, B., Absence of absolutely continuous spectrum for some one dimensional random but deterministic potentials. Ann. Inst. Henri Poincaré, 1985, 42, 383-406.
    • (1985) Ann. Inst. Henri Poincaré , vol.42 , pp. 383-406
    • Kirsch, W.1    Kotani, S.2    Simon, B.3
  • 14
    • 0001575233 scopus 로고
    • Jacobi matrices with random potentials taking finitely many values
    • Kotani, S., Jacobi matrices with random potentials taking finitely many values. Rev. Math. Phys., 1989, 1, 129-133.
    • (1989) Rev. Math. Phys. , vol.1 , pp. 129-133
    • Kotani, S.1
  • 15
    • 0042937447 scopus 로고
    • Singular continuous spectrum on a cantor set of zero lebesgue measure for the Fibonacci Hamiltonian
    • Süto, A., Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian. J. Stat. Phys., 1989, 56, 77-81.
    • (1989) J. Stat. Phys. , vol.56 , pp. 77-81
    • Süto, A.1
  • 16
    • 0002362803 scopus 로고
    • Anderson localization for Bernouilli and other singular potentials
    • Carmona, R., Klein, A. and Martinelli, F., Anderson localization for Bernouilli and other singular potentials. CMP, 1987, 108, 41-66.
    • (1987) CMP , vol.108 , pp. 41-66
    • Carmona, R.1    Klein, A.2    Martinelli, F.3
  • 17
    • 0000519980 scopus 로고
    • The new concept of transition by breaking of analyticity
    • Aubry, S., The new concept of transition by breaking of analyticity. Solid State Sci., 1978, 8, 264.
    • (1978) Solid State Sci. , vol.8 , pp. 264
    • Aubry, S.1
  • 18
    • 0001215377 scopus 로고
    • Analyticity breaking and anderson localization in incommensurate lattices
    • Andre, G. and Aubry, S., Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Israel Phys. Soc., 1980, 3, 133-164.
    • (1980) Ann. Israel Phys. Soc. , vol.3 , pp. 133-164
    • Andre, G.1    Aubry, S.2
  • 19
    • 84966202323 scopus 로고
    • Singular continuous spectrum for a class of almost periodic Jacobi matrices
    • Avron, J. and Simon, B., Singular continuous spectrum for a class of almost periodic Jacobi matrices. Bull. AMS, 1982, 6, 81-85.
    • (1982) Bull. AMS , vol.6 , pp. 81-85
    • Avron, J.1    Simon, B.2
  • 20
    • 0039738784 scopus 로고
    • Anderson localization for the almost Matheiu equation II. Point spectrum for ramda 2
    • Jitomirskaya, S. Ya., Anderson localization for the almost Matheiu equation II. Point spectrum for ramda 2. CMP, 1995, 168, 563-570.
    • (1995) CMP , vol.168 , pp. 563-570
    • Jitomirskaya, S.Ya.1
  • 21
    • 21844505868 scopus 로고
    • Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators
    • Jitomirskaya, S. Ya. and Simon, B., Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators. CMP, 1994, 165, 201-205.
    • (1994) CMP , vol.165 , pp. 201-205
    • Jitomirskaya, S.Ya.1    Simon, B.2
  • 22
    • 33847667155 scopus 로고
    • Zero measure spectrum for the almost Matheiu operator
    • Last, Y., Zero measure spectrum for the almost Matheiu operator. CMP, 1994, 164, 421-432.
    • (1994) CMP , vol.164 , pp. 421-432
    • Last, Y.1
  • 23
    • 0000532658 scopus 로고
    • Localization problem in one dimension: Mapping and escape
    • Kohmoto, M., Kadanoff, L. P. and Tang, Ch., Localization problem in one dimension: mapping and escape. Phys. Rev. Lett., 1983, 50, 1870-1872.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1870-1872
    • Kohmoto, M.1    Kadanoff, L.P.2    Tang, Ch.3
  • 25
    • 33846875539 scopus 로고
    • Spectral properties of one dimensional quasi-crystals
    • Bellissard, J., Iochum, B., Scoppola, E. and Testard, D., Spectral properties of one dimensional quasi-crystals. CMP, 1989, 125, 527-543.
    • (1989) CMP , vol.125 , pp. 527-543
    • Bellissard, J.1    Iochum, B.2    Scoppola, E.3    Testard, D.4
  • 26
    • 23644443660 scopus 로고    scopus 로고
    • Singular continuous spectrum for palidromic schrödinger operators
    • Hof, A., Knill, O. and Simon, B., Singular continuous spectrum for Palidromic Schrödinger operators. CMP.
    • CMP
    • Hof, A.1    Knill, O.2    Simon, B.3
  • 27
    • 84972583190 scopus 로고
    • Exponential localization in one dimensional disordered systems
    • Carmona, R., Exponential localization in one dimensional disordered systems. Duke Math. J., 1982, 49, 191-213.
    • (1982) Duke Math. J. , vol.49 , pp. 191-213
    • Carmona, R.1
  • 28
    • 0001518561 scopus 로고
    • One dimensional Schrödinger operators with random or deterministic potentials: New spectral types
    • Carmona, R., One dimensional Schrödinger operators with random or deterministic potentials: new spectral types. J. Funct. Anal., 1983, 51, 229-258.
    • (1983) J. Funct. Anal. , vol.51 , pp. 229-258
    • Carmona, R.1
  • 29
    • 0000328340 scopus 로고
    • Lyapunov exponents and spectra for one-dimensional random schrödinger operators
    • AMS, Providence, RI
    • Kotani, S., Lyapunov exponents and spectra for one-dimensional random Schrödinger operators. In Proc. Conf. on Random Matrices and their Applications in Contemporary Math. AMS, Providence, RI, 1986, Vol. 50, pp. 277-286.
    • (1986) Proc. Conf. on Random Matrices and Their Applications in Contemporary Math. , vol.50 , pp. 277-286
    • Kotani, S.1
  • 30
    • 0001346875 scopus 로고
    • Anderson localization for multidimensional systems at large disorder or low energy
    • Delyon, F., Levy, Y. and Souillard, B., Anderson localization for multidimensional systems at large disorder or low energy. CMP, 1985, 100, 463-470.
    • (1985) CMP , vol.100 , pp. 463-470
    • Delyon, F.1    Levy, Y.2    Souillard, B.3
  • 31
    • 84990576488 scopus 로고
    • Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians
    • Simon, B. and Wolff, T., Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Commun. Pure Appl. Math., 1986, 39, 75-90.
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 75-90
    • Simon, B.1    Wolff, T.2
  • 32
    • 0000284780 scopus 로고
    • Absence of diffusion in the Anderson tight binding model for large disorder or low energy
    • Fröhlich, J. and Spencer, T., Absence of diffusion in the Anderson tight binding model for large disorder or low energy. CMP, 1983, 88, 151-184.
    • (1983) CMP , vol.88 , pp. 151-184
    • Fröhlich, J.1    Spencer, T.2
  • 33
    • 0001758451 scopus 로고
    • Spectral analysis of rank one perturbations and applications
    • eds J. Feldman, R. Froese and L. M. Rosen. CRM Proc. and Lect. Notes, AMS, Providence, RI
    • Simon, B., Spectral analysis of rank one perturbations and applications. In Mathematical Quantum Theory II: Schrödinger Operators, eds J. Feldman, R. Froese and L. M. Rosen. CRM Proc. and Lect. Notes, AMS, Providence, RI, 1995, Vol. 8, pp. 109-149.
    • (1995) Mathematical Quantum Theory II: Schrödinger Operators , vol.8 , pp. 109-149
    • Simon, B.1
  • 34
    • 84972566320 scopus 로고
    • Almost periodic Schrödinger operators II. The integrated density of states
    • Avron, J. and Simon, B., Almost periodic Schrödinger operators II. The integrated density of states. Duke Math. J., 1983, 50, 369-391.
    • (1983) Duke Math. J. , vol.50 , pp. 369-391
    • Avron, J.1    Simon, B.2
  • 35
    • 34250399331 scopus 로고
    • The periodic problem for the Korteweg de Vries equation
    • Novikov, S. P., The periodic problem for the Korteweg de Vries equation. Funct. Anal. Appl., 1974, 8, 236-246.
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 236-246
    • Novikov, S.P.1
  • 36
    • 0001253693 scopus 로고
    • The spectrum of Hill's equation
    • McKean, H. P. and van Moerbeck, P., The spectrum of Hill's equation. Invent. Math., 1975, 30, 217-274.
    • (1975) Invent. Math. , vol.30 , pp. 217-274
    • McKean, H.P.1    Van Moerbeck, P.2
  • 37
    • 0038440059 scopus 로고
    • Spectral theory of a class of one dimensional Schrödinger operators with limit-periodic potentials
    • Pastur, L. A. and Tkachenko, B. A., Spectral theory of a class of one dimensional Schrödinger operators with limit-periodic potentials. Trans. Moscow Math. Soc., 1989, 51, 115-158.
    • (1989) Trans. Moscow Math. Soc. , vol.51 , pp. 115-158
    • Pastur, L.A.1    Tkachenko, B.A.2
  • 38
    • 0001316266 scopus 로고
    • Almost periodicity of some random potentials
    • Kotani, S. and Krishna, M., Almost periodicity of some random potentials. J. Funct. Anal., 1988, 78, 390-405.
    • (1988) J. Funct. Anal. , vol.78 , pp. 390-405
    • Kotani, S.1    Krishna, M.2
  • 39
    • 0000976339 scopus 로고
    • The trace formula for Schrödinger operators on the line
    • Craig, W., The trace formula for Schrödinger operators on the line. CMP, 1989, 126, 379-407.
    • (1989) CMP , vol.126 , pp. 379-407
    • Craig, W.1
  • 40
    • 51249169974 scopus 로고
    • Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum
    • Sodin, M. and Yuditskii, P., Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum. Comment Math. Helvetici, 1995, 70, 639-658.
    • (1995) Comment Math. Helvetici , vol.70 , pp. 639-658
    • Sodin, M.1    Yuditskii, P.2
  • 41
    • 0040517213 scopus 로고    scopus 로고
    • The ξ function
    • Gesztesy, F. and Simon, B., The ξ function. Acta Math., 1996, 176, 49-71.
    • (1996) Acta Math. , vol.176 , pp. 49-71
    • Gesztesy, F.1    Simon, B.2
  • 42
    • 0009977801 scopus 로고
    • On the inverse problem for random Schrödinger operators
    • Kotani, S., On the inverse problem for random Schrödinger operators. AMS Providence R.I., Contemporary Math., 1985, 41, 267-280.
    • (1985) AMS Providence R.I., Contemporary Math. , vol.41 , pp. 267-280
    • Kotani, S.1


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