메뉴 건너뛰기




Volumn 2, Issue 5, 2001, Pages 927-939

A Palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035648441     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-001-8599-9     Document Type: Article
Times cited : (12)

References (35)
  • 1
    • 0031476854 scopus 로고    scopus 로고
    • Schrödinger operators with Rudin-Shapiro potentials are not palindromic
    • J.-P. Allouche, Schrödinger operators with Rudin-Shapiro potentials are not palindromic, J. Math. Phys. 38, 1843-1848 (1997).
    • (1997) J. Math. Phys. , vol.38 , pp. 1843-1848
    • Allouche, J.-P.1
  • 2
    • 0000212740 scopus 로고    scopus 로고
    • A note on palindromicity
    • M. Baake, A note on palindromicity, Lett. Math. Phys. 49, 217-227 (1999).
    • (1999) Lett. Math. Phys. , vol.49 , pp. 217-227
    • Baake, M.1
  • 3
    • 0001719066 scopus 로고
    • Trace maps, invariants, and some of their applications
    • M. Baake, U. Grimm, and D. Joseph, Trace maps, invariants, and some of their applications, Int. J. Mod. Phys. B 7, 1527-1550 (1993).
    • (1993) Int. J. Mod. Phys. B , vol.7 , pp. 1527-1550
    • Baake, M.1    Grimm, U.2    Joseph, D.3
  • 4
    • 0040844827 scopus 로고    scopus 로고
    • Reversing symmetry group of GL(2, ℤ) and PGL(2, ℤ) matrices with connections to cat maps and trace maps
    • M. Baake and J. A. G. Roberts, Reversing symmetry group of GL(2, ℤ) and PGL(2, ℤ) matrices with connections to cat maps and trace maps, J. Phys. A 30, 1549-1573 (1997).
    • (1997) J. Phys. A , vol.30 , pp. 1549-1573
    • Baake, M.1    Roberts, J.A.G.2
  • 5
    • 0001531218 scopus 로고
    • Spectral properties of Schrödinger's operator with a Thue-Morse potential
    • Eds. J. M. Luck, P. Moussa and M. Waldschmidt, Springer, Berlin
    • J. Bellissard, Spectral properties of Schrödinger's operator with a Thue-Morse potential, in: Number Theory and Physics (Les Houches, 1989), Eds. J. M. Luck, P. Moussa and M. Waldschmidt, Springer, Berlin (1990), pp. 140-150.
    • (1990) Number Theory and Physics (Les Houches, 1989) , pp. 140-150
    • Bellissard, J.1
  • 6
    • 0000281159 scopus 로고
    • Spectral properties of a tight binding Hamiltonian with period doubling potential
    • J. Bellissard, A. Bovier, and J.-M. Ghez, 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
  • 7
    • 0001866286 scopus 로고
    • Gap labeling theorems for one-dimensional discrete Schrödinger operators
    • J. Bellissard, A. Bovier, and J.-M. Ghez, Gap labeling theorems for one-dimensional discrete Schrödinger operators, Rev. Math. Phys. 4, 1-37 (1992).
    • (1992) Rev. Math. Phys. , vol.4 , pp. 1-37
    • 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)
    • A. Bovier and J.-M. Ghez, 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
    • 0002380788 scopus 로고    scopus 로고
    • α-continuity properties of one-dimensional quasicrystals
    • D. Damanik, 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
  • 11
    • 0032336232 scopus 로고    scopus 로고
    • Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure
    • D. Damanik, 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
  • 12
    • 0001495933 scopus 로고    scopus 로고
    • Singular continuous spectrum for a class of substitution Hamiltonians
    • D. Damanik, Singular continuous spectrum for a class of substitution Hamiltonians, Lett. Math. Phys. 46, 303-311 (1998).
    • (1998) Lett. Math. Phys. , vol.46 , pp. 303-311
    • Damanik, D.1
  • 13
    • 0000918178 scopus 로고    scopus 로고
    • Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
    • Eds. M. Baake and R. V. Moody, CRM Monograph Series 13, AMS, Providence
    • D. Damanik, Gordon-type arguments in the spectral theory of one-dimensional quasicrystals, in: Directions in Mathematical Quasicrystals, Eds. M. Baake and R. V. Moody, CRM Monograph Series 13, AMS, Providence, R7, pp 277-304 (2000).
    • (2000) Directions in Mathematical Quasicrystals , vol.R7 , pp. 277-304
    • Damanik, D.1
  • 14
    • 0034664283 scopus 로고    scopus 로고
    • Substitution Hamiltonians with bounded trace map orbits
    • D. Damanik, Substitution Hamiltonians with bounded trace map orbits, J. Math. Anal. Appl. 249, 393-411 (2000).
    • (2000) J. Math. Anal. Appl. , vol.249 , pp. 393-411
    • Damanik, D.1
  • 15
    • 23044525988 scopus 로고    scopus 로고
    • Uniform singular continuous spectrum for the period doubling Hamiltonian
    • D. Damanik, 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
  • 16
    • 0007177363 scopus 로고    scopus 로고
    • Singular continuous spectrum for a class of substitution Hamiltonians II
    • D. Damanik, Singular continuous spectrum for a class of substitution Hamiltonians II., Lett. Math. Phys. 54, 25-31 (2000).
    • (2000) Lett. Math. Phys. , vol.54 , pp. 25-31
    • Damanik, D.1
  • 17
    • 0034349285 scopus 로고    scopus 로고
    • Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity
    • D. Damanik, R. Killip, and D. Lenz, 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
  • 18
    • 0033475027 scopus 로고    scopus 로고
    • Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues
    • D. Damanik and D. Lenz, Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues, Commun. Math. Phys. 207, 687-696 (1999).
    • (1999) Commun. Math. Phys. , vol.207 , pp. 687-696
    • Damanik, D.1    Lenz, D.2
  • 19
    • 0000796383 scopus 로고    scopus 로고
    • Palindrome complexity bounds for primitive substitution sequences
    • D. Damanik and D. Zare, Palindrome complexity bounds for primitive substitution sequences, Discrete Math. 222, 259-267 (2000).
    • (2000) Discrete Math. , vol.222 , pp. 259-267
    • Damanik, D.1    Zare, D.2
  • 20
    • 33846866830 scopus 로고
    • Absence of localization in a class of Schrödinger operators with quasiperiodic potential
    • F. Delyon and D. Petritis, Absence of localization in a class of Schrödinger operators with quasiperiodic potential, Commun. Math. Phys. 103, 441-444 (1986).
    • (1986) Commun. Math. Phys. , vol.103 , pp. 441-444
    • Delyon, F.1    Petritis, D.2
  • 21
    • 0000586806 scopus 로고
    • Recurrence of the eigenstates of a Schrödinger operator with automatic potential
    • F. Delyon, J. Peyrière, Recurrence of the eigenstates of a Schrödinger operator with automatic potential, J. Stat. Phys. 64, 363-368 (1991).
    • (1991) J. Stat. Phys. , vol.64 , pp. 363-368
    • Delyon, F.1    Peyrière, J.2
  • 22
    • 0000425895 scopus 로고
    • On the point spectrum of the one-dimensional Schrödinger operator
    • A. Gordon, On the point spectrum of the one-dimensional Schrödinger operator, Usp. Math. Nauk 31, 257-258 (1976).
    • (1976) Usp. Math. Nauk , vol.31 , pp. 257-258
    • Gordon, A.1
  • 23
    • 21844499250 scopus 로고
    • Singular continuous electron spectrum for a class of circle sequences
    • M. Hörnquist and M. Johansson, Singular continuous electron spectrum for a class of circle sequences, J. Phys. A 28, 479-495 (1995).
    • (1995) J. Phys. A , vol.28 , pp. 479-495
    • Hörnquist, M.1    Johansson, M.2
  • 24
    • 0000670801 scopus 로고
    • Singular continuous spectrum for palindromic Schrödinger operators
    • A. Hof, O. Knill, and B. Simon, 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
  • 25
    • 21844505868 scopus 로고
    • Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators
    • S. Jitomirskaya and B. Simon, Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators, Commun. Math. Phys. 165, 201-205 (1994).
    • (1994) Commun. Math. Phys. , vol.165 , pp. 201-205
    • Jitomirskaya, S.1    Simon, B.2
  • 26
    • 0001575233 scopus 로고
    • Jacobi matrices with random potentials taking finitely many values
    • S. Kotani, 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
  • 27
    • 0033074693 scopus 로고    scopus 로고
    • Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
    • Y. Last and B. Simon, 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
  • 28
    • 0000215231 scopus 로고
    • Cantor spectra and scaling of gap widths in deterministic aperi-odic systems
    • J.-M. Luck, Cantor spectra and scaling of gap widths in deterministic aperi-odic systems, Phys. Rev. B 39, 5834-5849 (1989).
    • (1989) Phys. Rev. B , vol.39 , pp. 5834-5849
    • Luck, J.-M.1
  • 29
    • 0003255477 scopus 로고
    • Substitution dynamical systems - Spectral analysis
    • Springer, Berlin, Heidelberg, New York
    • M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Mathematics, Vol. 1284, Springer, Berlin, Heidelberg, New York (1987).
    • (1987) Lecture Notes in Mathematics , vol.1284
    • Queffélec, M.1
  • 31
    • 0030164711 scopus 로고    scopus 로고
    • Escaping orbits in trace maps
    • J. A. G. Roberts, Escaping orbits in trace maps, Physica A 228, 295-325 (1996).
    • (1996) Physica A , vol.228 , pp. 295-325
    • Roberts, J.A.G.1
  • 32
    • 21344483960 scopus 로고
    • Trace maps as 3D reversible dynamical systems with an invariant
    • J. A. G. Roberts and M. Baake, Trace maps as 3D reversible dynamical systems with an invariant, J. Stat. Phys. 74, 829-888 (1994).
    • (1994) J. Stat. Phys. , vol.74 , pp. 829-888
    • Roberts, J.A.G.1    Baake, M.2
  • 33
    • 33751141500 scopus 로고
    • Metallic phase with long-range orientational order and no translational symmetry
    • D. Shechtman, I. Blech, D. Gratias, and J. V. Cahn, Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53, 1951-1953 (1984).
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 1951-1953
    • Shechtman, D.1    Blech, I.2    Gratias, D.3    Cahn, J.V.4
  • 34
    • 34250103530 scopus 로고
    • The spectrum of a quasiperiodic Schrödinger operator
    • A. Süto, 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
  • 35
    • 0042937447 scopus 로고
    • Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian
    • A. Süto, 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.