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Volumn 52, Issue 11, 2011, Pages

Erratum: Exponentially localized Wannier functions in periodic zero flux magnetic fields (Journal of Mathematical Physics (2011) 52 (112103) DOI: 10.1063/1.3657344);Exponentially localized Wannier functions in periodic zero flux magnetic fields

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EID: 82855169664     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/5.0021320     Document Type: Erratum
Times cited : (23)

References (58)
  • 3
    • 82855170289 scopus 로고    scopus 로고
    • Wannier transform for aperiodic tilings
    • (unpublished).
    • Bellissard J. De Nittis G. Milani V. Wannier transform for aperiodic tilings (unpublished).
    • Bellissard, J.1    De Nittis, G.2    Milani, V.3
  • 4
    • 0002886433 scopus 로고
    • Gap labelling theorems for Schrödinger operators
    • J.M.Luck, P.Moussa, M.Waldschmidt In, edited by and (Springer-Verlag, Berlin)
    • Bellissard J. Gap labelling theorems for Schrödinger operators. From Number Theory to Physics 1993, 538-630. J.M.Luck, P.Moussa, M.Waldschmidt In edited by and (Springer-Verlag, Berlin)
    • (1993) From Number Theory to Physics , pp. 538-630
    • Bellissard, J.1
  • 5
    • 33846500082 scopus 로고    scopus 로고
    • Exponential localization of Wannier functions in insulators
    • 10.1103/PhysRevLett.98.046402
    • Brouder C. Panati G. Calandra M. Mourougane C. Marzari N. Exponential localization of Wannier functions in insulators. Phys. Rev. Lett. 2007, 98(4):046402. 10.1103/PhysRevLett.98.046402
    • (2007) Phys. Rev. Lett. , vol.98 , Issue.4 , pp. 046402
    • Brouder, C.1    Panati, G.2    Calandra, M.3    Mourougane, C.4    Marzari, N.5
  • 7
    • 0001916219 scopus 로고
    • On the spectrum of gauge-periodic elliptic operators
    • Brüning J. Sunada T. On the spectrum of gauge-periodic elliptic operators. Astérisque 1992, 210:65-74
    • (1992) Astérisque , vol.210 , pp. 65-74
    • Brüning, J.1    Sunada, T.2
  • 8
    • 84972500756 scopus 로고
    • On the spectrum of periodic elliptic operators
    • Brüning J. Sunada T. On the spectrum of periodic elliptic operators. Nagoya Math. J. 1992, 126:159-171
    • (1992) Nagoya Math. J. , vol.126 , pp. 159-171
    • Brüning, J.1    Sunada, T.2
  • 9
    • 0000424033 scopus 로고
    • Nahm's transformation for instantons
    • 10.1007/BF01257416
    • Braam P.J. Van Baal P. Nahm's transformation for instantons. Commun. Math. Phys. 1989, 122(2):267-280. 10.1007/BF01257416
    • (1989) Commun. Math. Phys. , vol.122 , Issue.2 , pp. 267-280
    • Braam, P.J.1    Van Baal, P.2
  • 11
    • 84861399568 scopus 로고    scopus 로고
    • (European Mathematical Society, Zürich)
    • Dieck T.T. Algebraic Topology 2008, (European Mathematical Society, Zürich)
    • (2008) Algebraic Topology
    • Dieck, T.T.1
  • 12
    • 79955426418 scopus 로고    scopus 로고
    • Applications of magnetic ψDO techniques to SAPT - beyond a simple review
    • 10.1142/S0129055X11004278
    • De Nittis G. Lein M. Applications of magnetic ψDO techniques to SAPT - beyond a simple review. Rev. Math. Phys. 2011, 23:233-260. 10.1142/S0129055X11004278
    • (2011) Rev. Math. Phys. , vol.23 , pp. 233-260
    • De Nittis, G.1    Lein, M.2
  • 13
    • 82855170284 scopus 로고    scopus 로고
    • Magnetic symmetries
    • (unpublished).
    • De Nittis G. Lein M. Magnetic symmetries (unpublished).
    • De Nittis, G.1    Lein, M.2
  • 14
    • 0001225877 scopus 로고
    • Ground states of a two-dimensional electron in a periodic magnetic field
    • Dubrovin B.A. Novikov S.P. Ground states of a two-dimensional electron in a periodic magnetic field. Sov. Phys. JETP 1980, 52:511-516
    • (1980) Sov. Phys. JETP , vol.52 , pp. 511-516
    • Dubrovin, B.A.1    Novikov, S.P.2
  • 15
    • 79955430186 scopus 로고    scopus 로고
    • Effective models for conductance in magnetic fields: derivation of Harper and Hofstadter models
    • (submitted), arxiv:1007.4786.
    • De Nittis G. Panati G. Effective models for conductance in magnetic fields: derivation of Harper and Hofstadter models. 2010, (submitted), arxiv:1007.4786.
    • (2010)
    • De Nittis, G.1    Panati, G.2
  • 16
    • 82855174450 scopus 로고    scopus 로고
    • Complex vector bundles with trivial Chern classes on k-tori
    • MathOverflow (see)
    • Ekedahl T. Complex vector bundles with trivial Chern classes on k-tori. 2010 MathOverflow (see)
    • (2010)
    • Ekedahl, T.1
  • 20
    • 0000638506 scopus 로고
    • Analytische Faserungen Über holomorph-vollständigen Räumen
    • 10.1007/BF01351803
    • Grauert H. Analytische Faserungen Über holomorph-vollständigen Räumen. Math. Ann. 1958, 135:263-273. 10.1007/BF01351803
    • (1958) Math. Ann. , vol.135 , pp. 263-273
    • Grauert, H.1
  • 21
    • 0004193355 scopus 로고    scopus 로고
    • (Cambridge University Press, Cambridge, England)
    • Hatcher A. Algebraic Topology 2002, (Cambridge University Press, Cambridge, England)
    • (2002) Algebraic Topology
    • Hatcher, A.1
  • 22
    • 82855174197 scopus 로고    scopus 로고
    • Vector Bundles & K-Theory.
    • Hatcher A. 2009, Vector Bundles & K-Theory.
    • (2009)
    • Hatcher, A.1
  • 23
    • 82855170283 scopus 로고
    • Bands and gaps for periodic magnetic Hamiltonians
    • Hempel R. Herbst I. Bands and gaps for periodic magnetic Hamiltonians. Preprints ESI 1994, 162:1-11
    • (1994) Preprints ESI , vol.162 , pp. 1-11
    • Hempel, R.1    Herbst, I.2
  • 30
    • 36149021109 scopus 로고
    • Analytic properties of Bloch waves and Wannier functions
    • 10.1103/PhysRev.115.809
    • Kohn W. Analytic properties of Bloch waves and Wannier functions. Phys. Rev. 1959, 115:809-821. 10.1103/PhysRev.115.809
    • (1959) Phys. Rev. , vol.115 , pp. 809-821
    • Kohn, W.1
  • 31
    • 0003204788 scopus 로고
    • Floquet theory for partial differential equations
    • in (Birkhäuser, New York)
    • Kuchment P. Floquet theory for partial differential equations. Operator Theory: Advances and Applications 1993 in (Birkhäuser, New York)
    • (1993) Operator Theory: Advances and Applications
    • Kuchment, P.1
  • 32
    • 64549116230 scopus 로고    scopus 로고
    • Tight frames of exponentially decaying Wannier functions
    • 10.1088/1751-8113/42/2/025203
    • Kuchment P. Tight frames of exponentially decaying Wannier functions. J. Phys. A: Math. Theor. 2009, 42:025203. 10.1088/1751-8113/42/2/025203
    • (2009) J. Phys. A: Math. Theor. , vol.42 , pp. 025203
    • Kuchment, P.1
  • 33
    • 82855174451 scopus 로고    scopus 로고
    • M. S. thesis, Technische Universitüt München, Munich, Germany.
    • Lein M. 2005, M. S. thesis, Technische Universitüt München, Munich, Germany.
    • (2005)
    • Lein, M.1
  • 35
    • 12144266394 scopus 로고    scopus 로고
    • Vector Bundles and their Applications
    • (Kluwer Academic Publishers, Dordrecht)
    • Luke G. Mishchenko A.S. Vector Bundles and their Applications. Mathematics and Its Applications 1998, in (Kluwer Academic Publishers, Dordrecht)
    • (1998) Mathematics and Its Applications
    • Luke, G.1    Mishchenko, A.S.2
  • 39
    • 4243690324 scopus 로고    scopus 로고
    • Maximally localized generalized Wannier functions for composite energy bands
    • 10.1103/PhysRevB.56.12847
    • Marzari N. Vanderbilt D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 1997, 56:12847-12865. 10.1103/PhysRevB.56.12847
    • (1997) Phys. Rev. B , vol.56 , pp. 12847-12865
    • Marzari, N.1    Vanderbilt, D.2
  • 40
    • 0013032214 scopus 로고
    • Gauge potentials and bundles over the 4-torus
    • 10.1007/BF01213211
    • Nash C. Gauge potentials and bundles over the 4-torus. Commun. Math. Phys. 1983, 88:319-325. 10.1007/BF01213211
    • (1983) Commun. Math. Phys. , vol.88 , pp. 319-325
    • Nash, C.1
  • 41
    • 0002438025 scopus 로고
    • Existence of the exponentially localised Wannier functions
    • 10.1007/BF01206052
    • Nenciu G. Existence of the exponentially localised Wannier functions. Commun. Math. Phys. 1983, 91:81-85. 10.1007/BF01206052
    • (1983) Commun. Math. Phys. , vol.91 , pp. 81-85
    • Nenciu, G.1
  • 42
    • 12044249741 scopus 로고
    • Dynamics of band electrons in electric and magnetic fields: Rigorous justification of the effective Hamiltonians
    • 10.1103/RevModPhys.63.91
    • Nenciu G. Dynamics of band electrons in electric and magnetic fields: Rigorous justification of the effective Hamiltonians. Rev. Mod. Phys. 1991, 63(1):91-127. 10.1103/RevModPhys.63.91
    • (1991) Rev. Mod. Phys. , vol.63 , Issue.1 , pp. 91-127
    • Nenciu, G.1
  • 43
    • 0001505369 scopus 로고
    • Magnetic Bloch functions and vector bundles. Typical dispersion laws and their quantum numbers
    • Novikov S.P. Magnetic Bloch functions and vector bundles. Typical dispersion laws and their quantum numbers. Sov. Math. Dokl. 1981, 23:298-303.
    • (1981) Sov. Math. Dokl. , vol.23 , pp. 298-303
    • Novikov, S.P.1
  • 44
    • 34748863542 scopus 로고    scopus 로고
    • Triviality of Bloch and BlochâDirac bundles
    • 10.1007/s00023-007-0326-8
    • Panati G. Triviality of Bloch and BlochâDirac bundles. Ann. Henri Poincare 2007, 8:995-1011. 10.1007/s00023-007-0326-8
    • (2007) Ann. Henri Poincare , vol.8 , pp. 995-1011
    • Panati, G.1
  • 45
    • 0001197282 scopus 로고
    • Some remarks on Chern classes
    • 10.2307/1970191
    • Peterson F.P. Some remarks on Chern classes. Ann. Math. 1959, 69(2):414-420. 10.2307/1970191
    • (1959) Ann. Math. , vol.69 , Issue.2 , pp. 414-420
    • Peterson, F.P.1
  • 46
    • 79952028277 scopus 로고    scopus 로고
    • Disordered topological insulators: a non-commutative geometry perspective
    • Prodan E. Disordered topological insulators: a non-commutative geometry perspective. J. Phys. A: Math. Theor. 2011, 44:113001.
    • (2011) J. Phys. A: Math. Theor. , vol.44 , pp. 113001
    • Prodan, E.1
  • 47
    • 0344982977 scopus 로고    scopus 로고
    • Effective dynamics for Bloch electrons: Peierls substitution
    • 10.1007/s00220-003-0950-1
    • Panati G. Spohn H. Teufel S. Effective dynamics for Bloch electrons: Peierls substitution. Commun. Math. Phys. 2003, 242:547-578. 10.1007/s00220-003-0950-1
    • (2003) Commun. Math. Phys. , vol.242 , pp. 547-578
    • Panati, G.1    Spohn, H.2    Teufel, S.3
  • 48
    • 58849088108 scopus 로고    scopus 로고
    • Geometric currents in Piezoelectricity
    • 10.1007/s00205-008-0111-y
    • Panati G. Sparber C. Teufel S. Geometric currents in Piezoelectricity. Arch. Ration. Mech. Anal. 2009, 191:387-422. 10.1007/s00205-008-0111-y
    • (2009) Arch. Ration. Mech. Anal. , vol.191 , pp. 387-422
    • Panati, G.1    Sparber, C.2    Teufel, S.3
  • 51
    • 34250093202 scopus 로고
    • On a generalised fourier transform of instantons over flat tori
    • 10.1007/BF01225253
    • Schenk H. On a generalised fourier transform of instantons over flat tori. Commun. Math. Phys. 1988, 116(2):177-183. 10.1007/BF01225253
    • (1988) Commun. Math. Phys. , vol.116 , Issue.2 , pp. 177-183
    • Schenk, H.1
  • 52
    • 0001345770 scopus 로고
    • Holonomy, the quantum adiabatic theorem, and Berry's phase
    • 10.1103/PhysRevLett.51.2167
    • Simon B. Holonomy, the quantum adiabatic theorem, and Berry's phase. Phys. Rev. Lett. 1983, 51:2167-2170. 10.1103/PhysRevLett.51.2167
    • (1983) Phys. Rev. Lett. , vol.51 , pp. 2167-2170
    • Simon, B.1
  • 53
    • 77950788431 scopus 로고    scopus 로고
    • Absolute continuity of the spectrum of periodic operators of mathematical physics
    • Suslina T. Absolute continuity of the spectrum of periodic operators of mathematical physics. Journées Équations aux dérivées partielles 2000, XVIII:1-13.
    • (2000) Journées Équations aux dérivées partielles , vol.18 , pp. 1-13
    • Suslina, T.1
  • 54
    • 0000915510 scopus 로고
    • Wannier functions for magnetic sub-bands
    • 10.1088/0022-3719/17/12/003
    • Thouless D.J. Wannier functions for magnetic sub-bands. J. Phys. C 1984, 17:L325-L327. 10.1088/0022-3719/17/12/003
    • (1984) J. Phys. C , vol.17
    • Thouless, D.J.1
  • 55
    • 36149009855 scopus 로고
    • The structure of electronic excitation levels in insulating crystals
    • 10.1103/PhysRev.52.191
    • Wannier G.H. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 1937, 52:191-197. 10.1103/PhysRev.52.191
    • (1937) Phys. Rev. , vol.52 , pp. 191-197
    • Wannier, G.H.1
  • 56
    • 82855170280 scopus 로고    scopus 로고
    • Wannier Developers' Group, wannier.org.
    • 2011, Wannier Developers' Group, wannier.org.
    • (2011)
  • 57
    • 51249187120 scopus 로고
    • Theory of Bloch waves
    • 10.1007/BF02790171
    • Wilcox C. Theory of Bloch waves. J. Anal. Math. 1978, 33(1):146-167. 10.1007/BF02790171
    • (1978) J. Anal. Math. , vol.33 , Issue.1 , pp. 146-167
    • Wilcox, C.1
  • 58
    • 36149008019 scopus 로고
    • Magnetic translation group
    • 10.1103/PhysRev.134.A1602
    • Zak J. Magnetic translation group. Phys. Rev. 1964, 134(6A):A1602-A1606. 10.1103/PhysRev.134.A1602
    • (1964) Phys. Rev. , vol.134 , Issue.6 A
    • Zak, J.1


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