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Volumn 271, Issue , 2004, Pages 22-50

A non-commutative Landau-Zener formula

Author keywords

Energy level crossings; Landau Zener transitions; Multi scale convergence; Semi classical measures (Wigner measures)

Indexed keywords


EID: 4644253074     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310180     Document Type: Article
Times cited : (6)

References (27)
  • 1
    • 84972507638 scopus 로고
    • On the boundedness of pseudo-differential operators
    • A. P. Calderón and R. Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan 23, No. 2, 374-378 (1971).
    • (1971) J. Math. Soc. Japan , vol.23 , Issue.2 , pp. 374-378
    • Calderón, A.P.1    Vaillancourt, R.2
  • 3
    • 4644347038 scopus 로고    scopus 로고
    • The level crossing problem in semi-classical analysis. I. The symmetric case
    • Preprint, to appear in the, Annales de l'Institut Fourier
    • Y. Colin de Verdière, The level crossing problem in semi-classical analysis. I. The symmetric case, Preprint 2002, to appear in the Proceedings of Frédéric Pham's congress, Annales de l'Institut Fourier.
    • (2002) Proceedings of Frédéric Pham's Congress
    • Colin De Verdière, Y.1
  • 4
    • 0035537068 scopus 로고    scopus 로고
    • Avoided crossings in mesoscopic systems: Electron propagation on a non-uniform magnetic cylinder
    • P. Exner and A. Joye, Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder, Journal of Math. Physics 42, 4707-4738 (2001).
    • (2001) Journal of Math. Physics , vol.42 , pp. 4707-4738
    • Exner, P.1    Joye, A.2
  • 5
    • 0034288838 scopus 로고    scopus 로고
    • Mesures semi-classiques deux-microlocales
    • Série 1
    • C. Fermanian Kammerer, Mesures semi-classiques deux-microlocales, C. R. Acad. Sci. Paris 331, Série 1, 515-518 (2000).
    • (2000) C. R. Acad. Sci. Paris , vol.331 , pp. 515-518
    • Kammerer, C.F.1
  • 6
    • 0041724636 scopus 로고    scopus 로고
    • Propagation and absorption of concentration effects near shock hypersurfaces for the heat equation
    • C. Fermanian Kammerer, Propagation and absorption of concentration effects near shock hypersurfaces for the heat equation, Asymptotic Analysis 24, 107-141 (2000).
    • (2000) Asymptotic Analysis , vol.24 , pp. 107-141
    • Kammerer, C.F.1
  • 7
    • 85086291428 scopus 로고    scopus 로고
    • Mesures semi-classiques et croisements de modes
    • C. Fermanian Kammerer and P. Gerard, Mesures semi-classiques et croisements de modes, Bull. Soc. math. France 130 (1), 145-190 (2002).
    • (2002) Bull. Soc. Math. France , vol.130 , Issue.1 , pp. 145-190
    • Kammerer, C.F.1    Gerard, P.2
  • 8
    • 4644368579 scopus 로고    scopus 로고
    • Une formule de Landau- Zener pour un croisement générique de codimension
    • E.D.P., Exposé XXI
    • C. Fermanian Kammerer and P. Gérard, Une formule de Landau- Zener pour un croisement générique de codimension 2. Exposé de l'Ecole Polytechnique, E.D.P., Exposé XXI (2002).
    • (2002) 2. Exposé de l'Ecole Polytechnique
    • Kammerer, C.F.1    Gérard, P.2
  • 10
    • 0003495236 scopus 로고
    • Quantum mechanics and path integrals
    • edited by Maidenhead and Berksh. (McGraw-Hill Publishing Company)
    • R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, International Series in Pure and Applied Physics, edited by Maidenhead and Berksh. (McGraw-Hill Publishing Company, 1965).
    • (1965) International Series in Pure and Applied Physics
    • Feynman, R.P.1    Hibbs, A.R.2
  • 11
    • 0001342333 scopus 로고
    • Microlocal defect measures
    • P. Gérard, Microlocal defect measures, Comm. Part. Diff. Eq., 16, 1761-1794 (1991).
    • (1991) Comm. Part. Diff. Eq. , vol.16 , pp. 1761-1794
    • Gérard, P.1
  • 12
    • 0003072370 scopus 로고
    • Mesures semi-classiques et ondes de Bloch
    • E.D.P., Exposé XVI
    • P. Gérard, Mesures semi-classiques et ondes de Bloch, Exposé de l'Ecole Polytechnique, E.D.P., Exposé XVI (1991).
    • (1991) Exposé de l'Ecole Polytechnique
    • Gérard, P.1
  • 14
    • 0001206738 scopus 로고
    • Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps
    • G. A. Hagedorn, Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps, Commun. Math. Phys. 136, 433-449 (1991).
    • (1991) Commun. Math. Phys. , vol.136 , pp. 433-449
    • Hagedorn, G.A.1
  • 15
    • 0001118605 scopus 로고
    • Molecular propagation through electron energy level crossings
    • G. A. Hagedorn, Molecular propagation through electron energy level crossings, Memoirs of the Amer. Math. Soc. 111, No. 536 (1994).
    • (1994) Memoirs of the Amer. Math. Soc. , vol.111 , Issue.536
    • Hagedorn, G.A.1
  • 17
    • 0001778098 scopus 로고    scopus 로고
    • Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation
    • G. A. Hagedorn and A. Joye, Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation, Ann. Inst. Henri Poincaré, 68, No. 1, 85-134 (1998).
    • (1998) Ann. Inst. Henri Poincaré , vol.68 , Issue.1 , pp. 85-134
    • Hagedorn, G.A.1    Joye, A.2
  • 18
    • 0033477122 scopus 로고    scopus 로고
    • Molecular propagation through small avoided crossings of electron energy levels
    • G. A. Hagedorn and A. Joye, Molecular propagation through small avoided crossings of electron energy levels, Rev. Math. Phys. 1, No. 1, 41-101 (1999).
    • (1999) Rev. Math. Phys. , vol.1 , Issue.1 , pp. 41-101
    • Hagedorn, G.A.1    Joye, A.2
  • 19
    • 0028495271 scopus 로고
    • Proof of the Landau-Zener formula
    • A. Joye, Proof of the Landau-Zener formula, Asymptotic Analysis 9, 209-258 (1994).
    • (1994) Asymptotic Analysis , vol.9 , pp. 209-258
    • Joye, A.1
  • 22
    • 4644360923 scopus 로고    scopus 로고
    • Propagation d'onde semi-classiques à travers une interface et mesures 2-microlocales
    • L. Miller, Propagation d'onde semi-classiques à travers une interface et mesures 2-microlocales, Thèse de l'Ecole Polytechnique (1996).
    • (1996) Thèse de l'Ecole Polytechnique
    • Miller, L.1
  • 25
    • 0347112450 scopus 로고    scopus 로고
    • Semiclassical limit of the Dirac equation and spin precession
    • H. Spohn, Semiclassical limit of the Dirac equation and spin precession, Ann. physics 282, 2, 420-431 (2000).
    • (2000) Ann. Physics , vol.282 , Issue.2 , pp. 420-431
    • Spohn, H.1
  • 27
    • 0001332554 scopus 로고
    • Non-adiabatic crossing of energy levels
    • C. Zener, Non-adiabatic crossing of energy levels, Proc. Roy. Soc. Lond. 137, 696-702 (1932).
    • (1932) Proc. Roy. Soc. Lond. , vol.137 , pp. 696-702
    • Zener, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.