Ir al contenido

Documat


Spectral shift function for slowly varying perturbation of periodic Schrödinger operators

  • Mouez Dimassi [1] ; Maher Zerzeri [1]
    1. [1] Univ. Paris 13 LAGA
  • Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 1, 2012, págs. 29-47
  • Idioma: inglés
  • DOI: 10.4067/S0719-06462012000100004
  • Enlaces
  • Referencias bibliográficas
    • Alama, S,Deift, P-A,Hempel, R. (1989). Eigenvalue branches of the Schrödinger operator, Comm. Math. Phys. 121. 291-321
    • Birman, M-Sh,Yafaev, D-R. (1993). The spectral shift function. the papers of M-G. Krén and their further development. St. Petersburg Math....
    • Birman, M-Sh. (1995). The scattering matrix for a perturbation of a periodic Schrödinger operator by decreasing potential. St. Petersburg...
    • Buslaev, V-S. (1971). Scattered plane waves, spectral asymptotics and trace formulae in exterior problems, (Russian. Dokl. Akad. Nauk SSSR....
    • Buslaev, V-S. (1987). Semi-classical approximation for equations with periodic coeficients, Russian. Math. Surveys. 42. 97-125
    • Colin de Verdière, Y. (1981). Une formule de trace pour l'opérateur de Schrödinger dans R3. Ann. Ec. Normale Sup. 14. 27-39
    • Dimassi, M. (1993). Développements asymptotiques des perturbations lentes de l'opérateurr de Schrödinger périodique. Comm. Partial Differential...
    • Dimassi, M. (1998). Trace asymptotics formulas and some applications, Asymptot. Anal. 18. 1-32
    • Dimassi, M. (2002). Resonances for a slowly varying perturbation of a periodic Schrödinger operator. Canad. J. Math. 54. 998-1037
    • Dimassi, M. (2005). Spectral shift function and resonances for slowly varying perturbations of periodic Schrödinger operators. J. Funct. Anal....
    • Dimassi, M,Sjöstrand, J. (1999). Spectral asymptotics in the semi-classical limit. Cambridge University Press. Cambridge.
    • Dimassi, M,Zerzeri, M. (2003). A local trace formula for resonances of perturbed periodic Schrödinger operators. J. Funct. Anal. 198. 142-159
    • Gérard, C. (1990). Resonances theory for periodic Schrödinger operators. Bull.Soc.Math. France. 118. 27-54
    • Gérard, C. (2008). A proof of the abstract limiting absorption principle by energy estimates. J. Funct. Anal.. 254. 2707-2724
    • Gérard, C,Martinez, A,Sjöstrand, J. (1991). A mathematical approach to the effective hamiltonian in perturbed periodic problems. Comm. Math....
    • Gérard, C,Nier, F. (1998). Scattering theory for the perturbations of periodic Schrödinger operators. J. Math. Kyoto Univ. 38. 595-634
    • Guillopé, L. (1984). Asymptotique de la phase de difusion pour l'opérateur de Schrödinger dans Rn, Sém. E.D.P Ecole polytechnique, Exp....
    • Guillot, J-C,Ralston, J,Trubowitz, E. (1988). Semi-classical methods in solid state physics. Comm. Math. Phys. 116. 401-415
    • Helfer, B,Sjöstrand, J. (1989). Équation de Schrödinger avec champ magnétique et équation de harper, Schrödinger operators (Sönderborg, 1988....
    • Helfer, B. (1990). On diamagnetism and de haas-van alphen effect. Ann. Inst. H. Poincaré Phys. Thé or. 52. 303-375
    • Hôvermann, F,Spohn, H,Teufel, S. (2001). Semi-classical limit for the Schrödinger equation with a short scale periodic potential. Comm. Math....
    • Kreĭn, M-G.. (1953). On the trace formula in perturbation theory. (Russian. Mat. Sbornik N.S. 33. 597-626
    • Lifshits, I-M. (1952). On a problem in perturbation theory. (Russian. Uspekhi Mat. Nauk. 7. 171-180
    • Majda, A,Ralston, J. (1978). An analogue of Weyl's Theorem for unbounded domains. Duke Math. J.. 45. 183-196
    • Petkov, V,Popov, G. (1982). Asymptotic behavior of the scattering phase for non-trapping obstacles. Ann. Inst. Fourier Grenoble. 32. 111-149
    • Popov, G. (1982). Asymptotic behavior of the scattering phase for Schrödinger operator. Publ. Acad. Scien. Sofia. 35. 885-888
    • Reed, M,Simon, B. (1978). Methods of modern mathematical physics. IV, Academic Press. New York.
    • Robert, D. (1987). Autour de l'approximation semi-classique. Birkhäuser Boston, Inc. Boston.
    • Robert, D. (1991). Asymptotique à grande énergie de la phase de difusion pour un potentiel. Asymptotic Anal. 3. 301-320
    • Robert, D. (1992). Asymptotique de la phase de difusion à haute énergie pour des perturbations du second ordre du laplacien. Ann. Sci. école...
    • Robert, D. (1994). Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics. J. Funct. Anal. 126. 36-82
    • Robert, D. (1999). Semiclassical asymptotics for the spectral shift function. Amer. Math. Soc. Transl. 189. 187-203
    • Robert, D,Tamura, H. (1984). Semi-classical Bounds for Resolvents of Schrödinger Operators and Asymptotics for Scattering Phases. 9. 1017-1058
    • Robert, D. (1987). Semiclassical estimates for resolvents and asymptotics for total scattering cross-sections. Ann. Henri Poincaré Phys. Théor....
    • Robert, D. (1988). Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes. J. Funct. Anal....
    • Slater, J-C. (1949). Electrons in perturbed periodic lattices. Phys. Rev. 76. 1592-1600
    • Skriganov, M-M. (1985). The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential. Invent. Math. 80....
    • Skriganov, M-M. (1987). Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators, Russian A translation...
    • Sjöstrand, J. (1991). Microlocal analysis for the periodic magnetic Schrödinger equation and related questions, Microlocal analysis and applications...
    • Shubin, M-A. (1979). The spectral theory and the index of elliptic operators with almost periodic coeffcients. Russian Math. Surveys. 34....
    • Thomas, L-E. (1973). Time dependent approach to scattering from impurities in a crystal. Comm. Math. Phys. 33. 335-343
    • Yafaev, D. (2000). Scattering theory: some old and new problems, Scattering theory: some old and new problems. Lecture Notes in Math. 1737....
Los metadatos del artículo han sido obtenidos de SciELO Chile

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno