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Volumn 250, Issue 1, 2007, Pages 42-67

Spectral and propagation results for magnetic Schrödinger operators; A C*-algebraic framework

Author keywords

Dynamical system; Essential spectrum; Magnetic field; Pseudodifferential operators; Schr dinger operators; Twisted crossed product

Indexed keywords


EID: 34547127615     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.05.020     Document Type: Article
Times cited : (65)

References (44)
  • 3
    • 0001883347 scopus 로고
    • *-algebras in solid state physics
    • Statistical Mechanics and Field Theory: Mathematical Aspects. Groningen, 1985, Springer, Berlin
    • *-algebras in solid state physics. Statistical Mechanics and Field Theory: Mathematical Aspects. Groningen, 1985. Lecture Notes in Phys. vol. 257 (1986), Springer, Berlin 99-156
    • (1986) Lecture Notes in Phys. , vol.257 , pp. 99-156
    • Bellissard, J.1
  • 4
    • 0002886433 scopus 로고
    • Gap labelling theorems for Schrödinger operators
    • Les Houches, 1989, Springer, Berlin
    • Bellissard J. Gap labelling theorems for Schrödinger operators. From Number Theory to Physics. Les Houches, 1989 (1992), Springer, Berlin 538-630
    • (1992) From Number Theory to Physics , pp. 538-630
    • Bellissard, J.1
  • 5
    • 0000908661 scopus 로고
    • Representations of twisted group algebras
    • Busby R.C., and Smith H.A. Representations of twisted group algebras. Trans. Amer. Math. Soc. 149 (1970) 503-537
    • (1970) Trans. Amer. Math. Soc. , vol.149 , pp. 503-537
    • Busby, R.C.1    Smith, H.A.2
  • 7
    • 0005557893 scopus 로고
    • C-algebras of almost periodic pseudodifferential operators
    • Coburn L.A., Moyer R.D., and Singer I.M. C-algebras of almost periodic pseudodifferential operators. Acta Math. 130 (1973) 279-307
    • (1973) Acta Math. , vol.130 , pp. 279-307
    • Coburn, L.A.1    Moyer, R.D.2    Singer, I.M.3
  • 8
    • 0041193024 scopus 로고    scopus 로고
    • On eigenfunction decay for two-dimensional magnetic Schrödinger operators
    • Cornean H.D., and Nenciu G. On eigenfunction decay for two-dimensional magnetic Schrödinger operators. Comm. Math. Phys. 192 3 (1998) 671-685
    • (1998) Comm. Math. Phys. , vol.192 , Issue.3 , pp. 671-685
    • Cornean, H.D.1    Nenciu, G.2
  • 9
    • 0000527154 scopus 로고
    • Scattering theory for systems with different spatial asymptotics on the left and right
    • Davies E.B., and Simon B. Scattering theory for systems with different spatial asymptotics on the left and right. Comm. Math. Phys. 63 (1978) 277-301
    • (1978) Comm. Math. Phys. , vol.63 , pp. 277-301
    • Davies, E.B.1    Simon, B.2
  • 12
    • 0036022814 scopus 로고    scopus 로고
    • *-algebras and spectral analysis of quantum Hamiltonians
    • *-algebras and spectral analysis of quantum Hamiltonians. Comm. Math. Phys. 228 (2002) 519-560
    • (2002) Comm. Math. Phys. , vol.228 , pp. 519-560
    • Georgescu, V.1    Iftimovici, A.2
  • 14
    • 33745839349 scopus 로고    scopus 로고
    • Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory
    • Georgescu V., and Iftimovici A. Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory. Rev. Math. Phys. 18 4 (2006) 417-483
    • (2006) Rev. Math. Phys. , vol.18 , Issue.4 , pp. 417-483
    • Georgescu, V.1    Iftimovici, A.2
  • 15
    • 0002687246 scopus 로고
    • Caractérisation du spectre essentiel de l'opérateur de Schrödinger avec un champ magnétique
    • Helffer B., and Mohamed A. Caractérisation du spectre essentiel de l'opérateur de Schrödinger avec un champ magnétique. Ann. Inst. Fourier (Grenoble) 38 (1988) 95-112
    • (1988) Ann. Inst. Fourier (Grenoble) , vol.38 , pp. 95-112
    • Helffer, B.1    Mohamed, A.2
  • 16
    • 85008579665 scopus 로고
    • Examples of absolutely continuous Schrödinger operators in magnetic fields
    • Iwatsuka A. Examples of absolutely continuous Schrödinger operators in magnetic fields. Publ. Res. Inst. Math. Sci. 21 (1985) 385-401
    • (1985) Publ. Res. Inst. Math. Sci. , vol.21 , pp. 385-401
    • Iwatsuka, A.1
  • 17
    • 0035981884 scopus 로고    scopus 로고
    • Symplectic areas, quantization and dynamics in electromagnetic fields
    • Karasev M.V., and Osborn T.A. Symplectic areas, quantization and dynamics in electromagnetic fields. J. Math. Phys. 43 (2002) 756-788
    • (2002) J. Math. Phys. , vol.43 , pp. 756-788
    • Karasev, M.V.1    Osborn, T.A.2
  • 18
    • 1342347321 scopus 로고    scopus 로고
    • Quantum magnetic algebra and magnetic curvature
    • Karasev M.V., and Osborn T.A. Quantum magnetic algebra and magnetic curvature. J. Phys. A 37 (2004) 2345-2363
    • (2004) J. Phys. A , vol.37 , pp. 2345-2363
    • Karasev, M.V.1    Osborn, T.A.2
  • 19
    • 33748615986 scopus 로고    scopus 로고
    • The essential spectrum of Schrödinger, Jacobi and CMV operators
    • Last Y., and Simon B. The essential spectrum of Schrödinger, Jacobi and CMV operators. J. Anal. Math. 98 (2006) 183-220
    • (2006) J. Anal. Math. , vol.98 , pp. 183-220
    • Last, Y.1    Simon, B.2
  • 20
    • 0001669291 scopus 로고    scopus 로고
    • Analysis of geometric operators on open manifolds: A groupoid approach
    • Quantization of Singular Symplectic Quotients, Birkhäuser, Basel
    • Lauter R., and Nistor V. Analysis of geometric operators on open manifolds: A groupoid approach. Quantization of Singular Symplectic Quotients. Progr. Math. vol. 198 (2001), Birkhäuser, Basel 181-229
    • (2001) Progr. Math. , vol.198 , pp. 181-229
    • Lauter, R.1    Nistor, V.2
  • 21
    • 34547125419 scopus 로고
    • Dérivées intermédiaires et espaces intermédiaires
    • Lions J.-L. Dérivées intermédiaires et espaces intermédiaires. C. R. Acad. Sci. Paris 256 (1963) 4343-4345
    • (1963) C. R. Acad. Sci. Paris , vol.256 , pp. 4343-4345
    • Lions, J.-L.1
  • 22
    • 0043170908 scopus 로고    scopus 로고
    • *-algebras, dynamical systems at infinity and the essential spectrum of generalized Schrödinger operators
    • *-algebras, dynamical systems at infinity and the essential spectrum of generalized Schrödinger operators. J. Reine Angew. Math. 550 (2002) 211-229
    • (2002) J. Reine Angew. Math. , vol.550 , pp. 211-229
    • Mǎntoiu, M.1
  • 24
    • 33644633038 scopus 로고    scopus 로고
    • *-algebras that are independent with respect to a filter
    • *-algebras that are independent with respect to a filter. J. London Math. Soc. (2) 71 3 (2005) 740-758
    • (2005) J. London Math. Soc. (2) , vol.71 , Issue.3 , pp. 740-758
    • Mǎntoiu, M.1
  • 25
    • 0040453749 scopus 로고    scopus 로고
    • Some propagation properties of the Iwatsuka model
    • Mǎntoiu M., and Purice R. Some propagation properties of the Iwatsuka model. Comm. Math. Phys. 188 (1997) 691-708
    • (1997) Comm. Math. Phys. , vol.188 , pp. 691-708
    • Mǎntoiu, M.1    Purice, R.2
  • 26
    • 33749004085 scopus 로고    scopus 로고
    • The algebra of observables in a magnetic field
    • Mathematical Results in Quantum Mechanics. Taxco, 2001, Amer. Math. Soc., Providence, RI
    • Mǎntoiu M., and Purice R. The algebra of observables in a magnetic field. Mathematical Results in Quantum Mechanics. Taxco, 2001. Contemp. Math. vol. 307 (2002), Amer. Math. Soc., Providence, RI 239-245
    • (2002) Contemp. Math. , vol.307 , pp. 239-245
    • Mǎntoiu, M.1    Purice, R.2
  • 27
    • 2342421680 scopus 로고    scopus 로고
    • The magnetic Weyl calculus
    • Mǎntoiu M., and Purice R. The magnetic Weyl calculus. J. Math. Phys. 45 4 (2004) 1394-1417
    • (2004) J. Math. Phys. , vol.45 , Issue.4 , pp. 1394-1417
    • Mǎntoiu, M.1    Purice, R.2
  • 28
    • 33845977194 scopus 로고    scopus 로고
    • Twisted crossed products and magnetic pseudodifferential operators
    • Advances in Operator Algebras and Mathematical Physics, Theta, Bucharest
    • Mǎntoiu M., Purice R., and Richard S. Twisted crossed products and magnetic pseudodifferential operators. Advances in Operator Algebras and Mathematical Physics. Theta Ser. Adv. Math. vol. 5 (2005), Theta, Bucharest 137-172
    • (2005) Theta Ser. Adv. Math. , vol.5 , pp. 137-172
    • Mǎntoiu, M.1    Purice, R.2    Richard, S.3
  • 29
    • 18844382622 scopus 로고    scopus 로고
    • Strict deformation quantization for a particle in a variable magnetic field
    • 15 pp
    • Mǎntoiu M., and Purice R. Strict deformation quantization for a particle in a variable magnetic field. J. Math. Phys. 46 5 (2005) 052105 15 pp
    • (2005) J. Math. Phys. , vol.46 , Issue.5 , pp. 052105
    • Mǎntoiu, M.1    Purice, R.2
  • 30
    • 0039527297 scopus 로고    scopus 로고
    • Product rule for gauge invariant Weyl symbols and its applications to the semiclassical description of guiding center motion
    • Müller M. Product rule for gauge invariant Weyl symbols and its applications to the semiclassical description of guiding center motion. J. Phys. A 32 (1999) 1035-1052
    • (1999) J. Phys. A , vol.32 , pp. 1035-1052
    • Müller, M.1
  • 31
    • 0035981857 scopus 로고    scopus 로고
    • On asymptotic perturbation theory for quantum mechanics: Almost invariant subspaces and gauge invariant magnetic perturbation theory
    • Nenciu G. On asymptotic perturbation theory for quantum mechanics: Almost invariant subspaces and gauge invariant magnetic perturbation theory. J. Math. Phys. 43 3 (2002) 1273-1298
    • (2002) J. Math. Phys. , vol.43 , Issue.3 , pp. 1273-1298
    • Nenciu, G.1
  • 32
    • 33745847421 scopus 로고    scopus 로고
    • Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains
    • Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds. Roskilde University, Amer. Math. Soc., Providence, RI
    • Nistor V. Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains. Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds. Roskilde University. Contemp. Math. (2005), Amer. Math. Soc., Providence, RI 307-328
    • (2005) Contemp. Math. , pp. 307-328
    • Nistor, V.1
  • 35
    • 0037000949 scopus 로고    scopus 로고
    • On the essential spectrum of the relativistic magnetic operator
    • Pascu M. On the essential spectrum of the relativistic magnetic operator. Osaka J. Math. 39 (2002) 963-978
    • (2002) Osaka J. Math. , vol.39 , pp. 963-978
    • Pascu, M.1
  • 36
    • 15844419409 scopus 로고    scopus 로고
    • Essential spectrum of perturbed pseudo-differential operators. Applications to Scrödinger, Klein-Gordon and Dirac operators
    • Rabinovich V.S. Essential spectrum of perturbed pseudo-differential operators. Applications to Scrödinger, Klein-Gordon and Dirac operators. Russian J. Math. Phys. 12 (2005) 62-80
    • (2005) Russian J. Math. Phys. , vol.12 , pp. 62-80
    • Rabinovich, V.S.1
  • 39
    • 33749408303 scopus 로고    scopus 로고
    • Limit Operators and Their Applications in Operator Theory
    • Birkhäuser, Basel
    • Rabinovich V.S., Roch S., and Silbermann B. Limit Operators and Their Applications in Operator Theory. Oper. Theory Adv. Appl. vol. 150 (2004), Birkhäuser, Basel
    • (2004) Oper. Theory Adv. Appl. , vol.150
    • Rabinovich, V.S.1    Roch, S.2    Silbermann, B.3
  • 41
    • 19944370799 scopus 로고    scopus 로고
    • Spectral and scattering theory for Schrödinger operators with Cartesian anisotropy
    • Richard S. Spectral and scattering theory for Schrödinger operators with Cartesian anisotropy. Publ. Res. Inst. Math. Sci. 41 (2005) 73-111
    • (2005) Publ. Res. Inst. Math. Sci. , vol.41 , pp. 73-111
    • Richard, S.1
  • 43
    • 84957149530 scopus 로고
    • The spectral theory and the index of elliptic operators with almost periodic coefficients
    • Shubin M.A. The spectral theory and the index of elliptic operators with almost periodic coefficients. Russian Math. Surveys 34 (1979) 109-157
    • (1979) Russian Math. Surveys , vol.34 , pp. 109-157
    • Shubin, M.A.1
  • 44
    • 33646045148 scopus 로고
    • Unbounded Elements Affiliated with C-algebras and non compact quantum groups
    • Woronowicz S.L. Unbounded Elements Affiliated with C-algebras and non compact quantum groups. Comm. Math. Phys. 136 (1991) 399-432
    • (1991) Comm. Math. Phys. , vol.136 , pp. 399-432
    • Woronowicz, S.L.1


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