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Volumn 236, Issue 3, 2003, Pages 513-534

Power-law bounds on transfer matrices and quantum dynamics in one dimension

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EID: 0038239329     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0824-6     Document Type: Article
Times cited : (40)

References (40)
  • 1
    • 0001633387 scopus 로고
    • Spectrum and extended states in a harmonic chain with controlled disorder: Effects of the Thue-Morse symmetry
    • Axel, F., Peyrière, J.: Spectrum and extended states in a harmonic chain with controlled disorder: Effects of the Thue-Morse symmetry. J. Statist. Phys. 57, 1013-104 (1989)
    • (1989) J. Statist. Phys. , vol.57 , pp. 1013-1104
    • Axel, F.1    Peyrière, J.2
  • 2
    • 0031220833 scopus 로고    scopus 로고
    • Remarks on the relation between quantum dynamics and fractal spectra
    • Barbaroux, J.M., Combes, J.M., Montcho, R.: Remarks on the relation between quantum dynamics and fractal spectra. J. Math. Anal. Appl. 213, 698-72 (1997)
    • (1997) J. Math. Anal. Appl. , vol.213 , pp. 698-772
    • Barbaroux, J.M.1    Combes, J.M.2    Montcho, R.3
  • 4
    • 0000938886 scopus 로고    scopus 로고
    • Fractal dimensions and the phenomenon of intermittency in quantum dynamics
    • Barbaroux, J.M., Germinet, F., Tcheremchantsev, S.: Fractal dimensions and the phenomenon of intermittency in quantum dynamics. Duke Math. J. 110, 161-193 (2001)
    • (2001) Duke Math. J. , vol.110 , pp. 161-193
    • Barbaroux, J.M.1    Germinet, F.2    Tcheremchantsev, S.3
  • 5
    • 0035604405 scopus 로고    scopus 로고
    • Generalized fractal dimensions: Equivalences and basic properties
    • Barbaroux, J.M., Germinet, F., Tcheremchantsev, S.: Generalized fractal dimensions: Equivalences and basic properties. J. Math. Pures Appl. 80, 977-1012 (2001)
    • (2001) J. Math. Pures Appl. , vol.80 , pp. 977-1012
    • Barbaroux, J.M.1    Germinet, F.2    Tcheremchantsev, S.3
  • 6
    • 0001531218 scopus 로고
    • Spectral properties of Schrödinger's operator with a Thue-Morse potential
    • Number Theory and Physics (Les Houches, 1989), Berlin: Springer
    • Bellissard, J.: Spectral properties of Schrödinger's operator with a Thue-Morse potential. In: Number Theory and Physics (Les Houches, 1989), Springer Proc. Phys. 47, Berlin: Springer, 1990, pp. 140-150
    • (1990) Springer Proc. Phys. , vol.47 , pp. 140-150
    • Bellissard, J.1
  • 7
    • 0000281159 scopus 로고
    • Spectral properties of a tight binding Hamiltonian with period doubling potential
    • Bellissard, J., Bovier, A., Ghez, J.-M.: Spectral properties of a tight binding Hamiltonian with period doubling potential. Commun. Math. Phys. 135, 379-399 (1991)
    • (1991) Commun. Math. Phys. , vol.135 , pp. 379-399
    • Bellissard, J.1    Bovier, A.2    Ghez, J.-M.3
  • 9
    • 21344478675 scopus 로고
    • Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions
    • Erratum Commun. Math. Phys. 166, 431-432 (1994)
    • Bovier, A., Ghez, J.-M.: Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions. Commun. Math. Phys. 158, 45-66 (1993); Erratum Commun. Math. Phys. 166, 431-432 (1994)
    • (1993) Commun. Math. Phys. , vol.158 , pp. 45-66
    • Bovier, A.1    Ghez, J.-M.2
  • 10
    • 77956813912 scopus 로고
    • Connections between quantum dynamics and spectral properties of time-evolution operators
    • W.F. Ames, E.M. Harrel II, J.V. Herod (eds.), Academic Press, Boston
    • Combes, J.M.: Connections between quantum dynamics and spectral properties of time-evolution operators. In: Differential Equations with Applications to Mathematical Physics, W.F. Ames, E.M. Harrel II, J.V. Herod (eds.), Academic Press, Boston, 1993, pp. 59-68
    • (1993) Differential Equations with Applications to Mathematical Physics , pp. 59-68
    • Combes, J.M.1
  • 11
    • 0002380788 scopus 로고    scopus 로고
    • α-continuity properties of one-dimensional quasicrystals
    • Damanik, D.: α-continuity properties of one-dimensional quasicrystals. Commun. Math. Phys. 192, 169-182 (1998)
    • (1998) Commun. Math. Phys. , vol.192 , pp. 169-182
    • Damanik, D.1
  • 12
    • 0032336232 scopus 로고    scopus 로고
    • Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure
    • Damanik, D.: Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure. Commun. Math. Phys. 196, 477-483 (1998)
    • (1998) Commun. Math. Phys. , vol.196 , pp. 477-483
    • Damanik, D.1
  • 13
    • 0000918178 scopus 로고    scopus 로고
    • Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
    • Directions in Mathematical Quasicrystals, M. Baake, R.V. Moody (eds.), AMS, Providence, RI
    • Damanik, D.: Gordon-type arguments in the spectral theory of one-dimensional quasicrystals. In: Directions in Mathematical Quasicrystals, M. Baake, R.V. Moody (eds.), CRM Monograph Series 13, AMS, Providence, RI 2000, pp. 277-305
    • (2000) CRM Monograph Series , vol.13 , pp. 277-305
    • Damanik, D.1
  • 14
    • 23044525988 scopus 로고    scopus 로고
    • Uniform singular continuous spectrum for the period doubling Hamiltonian
    • Damanik, D.: Uniform singular continuous spectrum for the period doubling Hamiltonian. Ann. Henri Poincaré 2, 101-108 (2001)
    • (2001) Ann. Henri Poincaré , vol.2 , pp. 101-108
    • Damanik, D.1
  • 15
    • 0034349285 scopus 로고    scopus 로고
    • Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity
    • Damanik, D., Killip, R., Lenz, D.: Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity. Commun. Math. Phys. 212, 191-204 (2000)
    • (2000) Commun. Math. Phys. , vol.212 , pp. 191-204
    • Damanik, D.1    Killip, R.2    Lenz, D.3
  • 17
    • 0000586806 scopus 로고
    • Recurrence of the eigenstates of a Schrödinger operator with automatic potential
    • Delyon, F., Peyrière, J.: Recurrence of the eigenstates of a Schrödinger operator with automatic potential. J. Statist. Phys. 64, 363-368 (1991)
    • (1991) J. Statist. Phys. , vol.64 , pp. 363-368
    • Delyon, F.1    Peyrière, J.2
  • 18
    • 0003840368 scopus 로고
    • John Wiley & Sons, Ltd., Chichester
    • Falconer, K.: Fractal Geometry, John Wiley & Sons, Ltd., Chichester, 1990
    • (1990) Fractal Geometry
    • Falconer, K.1
  • 20
    • 84956097442 scopus 로고
    • Spectral properties of quantum diffusion on discrete lattices
    • Guarneri, I.: Spectral properties of quantum diffusion on discrete lattices. Europhys. Lett. 10, 95-100 (1989)
    • (1989) Europhys. Lett. , vol.10 , pp. 95-100
    • Guarneri, I.1
  • 21
    • 0003232182 scopus 로고    scopus 로고
    • Lower bounds on wave packet propagation by packing dimensions of spectral measures
    • Guarneri, I., Schulz-Baldes, H.: Lower bounds on wave packet propagation by packing dimensions of spectral measures. Math. Phys. Electron. J. 5(1), 16 (1999)
    • (1999) Math. Phys. Electron. J. , vol.5 , Issue.1 , pp. 16
    • Guarneri, I.1    Schulz-Baldes, H.2
  • 22
    • 0000881439 scopus 로고    scopus 로고
    • Intermittent lower bound on quantum diffusion
    • Guarneri, I., Schulz-Baldes, H.: Intermittent lower bound on quantum diffusion. Lett. Math. Phys. 49, 317-324 (1999)
    • (1999) Lett. Math. Phys. , vol.49 , pp. 317-324
    • Guarneri, I.1    Schulz-Baldes, H.2
  • 23
    • 0000670801 scopus 로고
    • Singular continuous spectrum for palindromic Schrödinger operators
    • Hof, A., Knill, O., Simon, B.: Singular continuous spectrum for palindromic Schrödinger operators. Commun. Math. Phys. 174, 149-159 (1995)
    • (1995) Commun. Math. Phys. , vol.174 , pp. 149-159
    • Hof, A.1    Knill, O.2    Simon, B.3
  • 24
    • 33845261621 scopus 로고
    • Power law growth for the resistance in the Fibonacci model
    • Iochum, B., Testard, D.: Power law growth for the resistance in the Fibonacci model. J. Stat. Phys. 65, 715-723 (1991)
    • (1991) J. Stat. Phys. , vol.65 , pp. 715-723
    • Iochum, B.1    Testard, D.2
  • 25
    • 0001666109 scopus 로고    scopus 로고
    • Power-law subordinacy and singular spectra. I. Half-line operators
    • Jitomirskaya, S., Last, Y.: Power-law subordinacy and singular spectra. I. Half-line operators. Acta Math. 183, 171-189 (1999)
    • (1999) Acta Math. , vol.183 , pp. 171-189
    • Jitomirskaya, S.1    Last, Y.2
  • 26
    • 0034348973 scopus 로고    scopus 로고
    • Power-law subordinacy and singular spectra. II. Line operators
    • Jitomirskaya, S., Last, Y.: Power-law subordinacy and singular spectra. II. Line operators. Commun. Math. Phys. 211, 643-658 (2000)
    • (2000) Commun. Math. Phys. , vol.211 , pp. 643-658
    • Jitomirskaya, S.1    Last, Y.2
  • 29
    • 0034652879 scopus 로고    scopus 로고
    • Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains
    • Kiselev, A., Last, Y.: Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains. Duke Math. J. 102, 125-150 (2000)
    • (2000) Duke Math. J. , vol.102 , pp. 125-150
    • Kiselev, A.1    Last, Y.2
  • 30
    • 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. 1, 129-133 (1989)
    • (1989) Rev. Math. Phys. , vol.1 , pp. 129-133
    • Kotani, S.1
  • 31
    • 0030589769 scopus 로고    scopus 로고
    • Quantum dynamics and decompositions of singular continuous spectra
    • Last, Y: Quantum dynamics and decompositions of singular continuous spectra. J. Funct. Anal. 142, 406-445 (1996)
    • (1996) J. Funct. Anal. , vol.142 , pp. 406-445
    • Last, Y.1
  • 32
    • 0033074693 scopus 로고    scopus 로고
    • Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
    • Last, Y., Simon, B.: Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators. Invent. Math. 135, 329-367 (1999)
    • (1999) Invent. Math. , vol.135 , pp. 329-367
    • Last, Y.1    Simon, B.2
  • 35
    • 21444433761 scopus 로고    scopus 로고
    • Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
    • Simon, B.: Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators. Proc. Am. Math. Soc. 124, 3361-3369 (1996)
    • (1996) Proc. Am. Math. Soc. , vol.124 , pp. 3361-3369
    • Simon, B.1
  • 36
    • 84990576488 scopus 로고
    • Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians
    • Simon, B., Wolff, T.: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Commun. Pure Appl. Math, 39, 75-90 (1986)
    • (1986) Commun. Pure Appl. Math , vol.39 , pp. 75-90
    • Simon, B.1    Wolff, T.2
  • 37
    • 34250103530 scopus 로고
    • The spectrum of a quasiperiodic Schrödinger operator
    • Süto, A.: The spectrum of a quasiperiodic Schrödinger operator. Commun. Math. Phys. 111, 409-415 (1987)
    • (1987) Commun. Math. Phys. , vol.111 , pp. 409-415
    • Süto, A.1
  • 38
    • 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. 56, 525-531 (1989)
    • (1989) J. Stat. Phys. , vol.56 , pp. 525-531
    • Süto, A.1
  • 39
    • 85064301341 scopus 로고    scopus 로고
    • Mixed lower bounds for quantum transport
    • Tcheremchantsev, S.: Mixed lower bounds for quantum transport. To appear in J. Funct. Anal.
    • J. Funct. Anal.
    • Tcheremchantsev, S.1


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