메뉴 건너뛰기




Volumn 194, Issue 3-4, 2004, Pages 250-274

Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields

Author keywords

Crossed electric and magnetic field; Hamiltonian Hopf bifurcation; Monodromy; Zeeman and Stark limit

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); ELECTRIC FIELDS; HAMILTONIANS; MAGNETIC FIELDS; MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES; POISSON DISTRIBUTION; VECTORS;

EID: 2942585296     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.03.003     Document Type: Article
Times cited : (29)

References (34)
  • 1
    • 23044508741 scopus 로고
    • Derivation and quantisation of Solov'ev's constant for the diamagnetic Kepler motion
    • Kuwata M., Harada A., Hasegawa H., Derivation and quantisation of Solov'ev's constant for the diamagnetic Kepler motion. J. Phys. A. 23(14):1990;3227-3244.
    • (1990) J. Phys. A , vol.23 , Issue.14 , pp. 3227-3244
    • Kuwata, M.1    Harada, A.2    Hasegawa, H.3
  • 2
    • 0043161218 scopus 로고
    • Dynamical symmetry of the quadratic Zeeman effect in hydrogen: Semiclassical quantization
    • Farrelly D., Krantzman K., Dynamical symmetry of the quadratic Zeeman effect in hydrogen: semiclassical quantization. Phys. Rev. A. 43:1991;1666-1668.
    • (1991) Phys. Rev. A , vol.43 , pp. 1666-1668
    • Farrelly, D.1    Krantzman, K.2
  • 3
    • 0043161231 scopus 로고
    • Semiclassical mechanics of the quadratic Zeeman effect
    • Krantzman K.D., Milligan J.A., Farrelly D., Semiclassical mechanics of the quadratic Zeeman effect. Phys. Rev. A. 45:1992;3093-3103.
    • (1992) Phys. Rev. A , vol.45 , pp. 3093-3103
    • Krantzman, K.D.1    Milligan, J.A.2    Farrelly, D.3
  • 4
    • 0009209977 scopus 로고
    • Action-angle variables for the diamagnetic Kepler problem
    • Farrelly D., Milligan J.A., Action-angle variables for the diamagnetic Kepler problem. Phys. Rev. A. 45:1992;8277-8279.
    • (1992) Phys. Rev. A , vol.45 , pp. 8277-8279
    • Farrelly, D.1    Milligan, J.A.2
  • 5
    • 0001580637 scopus 로고
    • Electronic structure of Rydberg atoms in parallel electric and magnetic fields
    • Farrelly D., Uzer T., Raines P.E., Skelton J.P., Milligan J.A., Electronic structure of Rydberg atoms in parallel electric and magnetic fields. Phys. Rev. A. 45:1992;4738-4751.
    • (1992) Phys. Rev. A , vol.45 , pp. 4738-4751
    • Farrelly, D.1    Uzer, T.2    Raines, P.E.3    Skelton, J.P.4    Milligan, J.A.5
  • 6
    • 0001739654 scopus 로고    scopus 로고
    • Collapse of the Zeeman structure of the hydrogen atom in an external electric field
    • Sadovskií D.A., Zhilinskií B.I., Michel L., Collapse of the Zeeman structure of the hydrogen atom in an external electric field. Phys. Rev. A. 53:1996;4064-4067.
    • (1996) Phys. Rev. A , vol.53 , pp. 4064-4067
    • Sadovskií, D.A.1    Zhilinskií, B.I.2    Michel, L.3
  • 7
    • 0000739702 scopus 로고    scopus 로고
    • Tuning the hydrogen atom in crossed fields between the Zeeman and Stark limits
    • Sadovskií D.A., Zhilinskií B.I., Tuning the hydrogen atom in crossed fields between the Zeeman and Stark limits. Phys. Rev. A. 57:1998;2867-2884.
    • (1998) Phys. Rev. A , vol.57 , pp. 2867-2884
    • Sadovskií, D.A.1    Zhilinskií, B.I.2
  • 8
    • 20444373406 scopus 로고    scopus 로고
    • Organization and bifurcation of planar closed orbits of an atomic electron in crossed fields
    • Wang D.M., Delos J.B., Organization and bifurcation of planar closed orbits of an atomic electron in crossed fields. Phys. Rev. A. 63:2001;43409-43422.
    • (2001) Phys. Rev. A , vol.63 , pp. 43409-43422
    • Wang, D.M.1    Delos, J.B.2
  • 9
    • 4243724024 scopus 로고    scopus 로고
    • Closed orbits and their bifurcations in the crossed-field hydrogen atom
    • Bartsch T., Main J., Wunner G., Closed orbits and their bifurcations in the crossed-field hydrogen atom. Phys. Rev. A. 67:2003;063410.
    • (2003) Phys. Rev. A , vol.67 , pp. 063410
    • Bartsch, T.1    Main, J.2    Wunner, G.3
  • 10
    • 0347450519 scopus 로고    scopus 로고
    • Monodromy in the hydrogen atom in crossed fields
    • Cushman R.H., Sadovskií D.A., Monodromy in the hydrogen atom in crossed fields. Physica D. 142:2000;166-196.
    • (2000) Physica D , vol.142 , pp. 166-196
    • Cushman, R.H.1    Sadovskií, D.A.2
  • 11
    • 0033153845 scopus 로고    scopus 로고
    • Monodromy perturbed Kepler systems: Hydrogen atom in crossed fields
    • Cushman R.H., Sadovskií D.A., Monodromy perturbed Kepler systems: hydrogen atom in crossed fields. Europhys. Lett. 47:1999;1-7.
    • (1999) Europhys. Lett. , vol.47 , pp. 1-7
    • Cushman, R.H.1    Sadovskií, D.A.2
  • 12
    • 0038515348 scopus 로고    scopus 로고
    • Quantum monodromy in the two-centre problem
    • Waalkens H., Junge A., Dullin H.R., Quantum monodromy in the two-centre problem. J. Phys. A. 36:2003;L307-L314.
    • (2003) J. Phys. A , vol.36
    • Waalkens, H.1    Junge, A.2    Dullin, H.R.3
  • 13
    • 84936358059 scopus 로고
    • Perturbation theory of Kepler motion based on spinor regularization
    • Kustaanheimo P., Stiefel E., Perturbation theory of Kepler motion based on spinor regularization. J. Reine Angew. Math. 219:1965;204-219.
    • (1965) J. Reine Angew. Math. , vol.219 , pp. 204-219
    • Kustaanheimo, P.1    Stiefel, E.2
  • 15
    • 0009206017 scopus 로고
    • A survey of normalization techniques applied to perturbed Keplerian systems
    • K. Jones et al. (Ed.), Springer-Verlag, New York
    • R.H. Cushman, A survey of normalization techniques applied to perturbed Keplerian systems, in: K. Jones, et al. (Ed.), Dynamics Reported, vol. 1 of new series, Springer-Verlag, New York, 1991, pp. 54-112.
    • (1991) Dynamics Reported, Vol. 1 of New Series , vol.1 , pp. 54-112
    • Cushman, R.H.1
  • 16
    • 0043067820 scopus 로고    scopus 로고
    • Chaos and order in crossed fields
    • von Milczewski J., Uzer T., Chaos and order in crossed fields. Phys. Rev. E. 55:1997;6540-6551.
    • (1997) Phys. Rev. E , vol.55 , pp. 6540-6551
    • Von Milczewski, J.1    Uzer, T.2
  • 18
    • 0011640874 scopus 로고    scopus 로고
    • Role of the atomic Coulomb center in ionization and periodic orbit selection
    • von Milczewski J., Farrelly D., Uzer T., Role of the atomic Coulomb center in ionization and periodic orbit selection. Phys. Rev. A. 56:1997;657-670.
    • (1997) Phys. Rev. A , vol.56 , pp. 657-670
    • Von Milczewski, J.1    Farrelly, D.2    Uzer, T.3
  • 20
    • 0000717287 scopus 로고
    • Canonical transformations depending on a small parameter
    • Deprit A., Canonical transformations depending on a small parameter. Cel. Mech. 1:1969;12-30.
    • (1969) Cel. Mech. , vol.1 , pp. 12-30
    • Deprit, A.1
  • 21
    • 84980167278 scopus 로고
    • On global action-angle coordinates
    • Duistermaat J.J., On global action-angle coordinates. Commun. Pure Appl. Math. 33:1980;687-706.
    • (1980) Commun. Pure Appl. Math. , vol.33 , pp. 687-706
    • Duistermaat, J.J.1
  • 23
    • 0003349147 scopus 로고
    • The hamiltonian hopf bifurcation
    • Springer, New York
    • J.C. van der Meer, The Hamiltonian Hopf Bifurcation, vol. 1160 of Lecture Notes in Mathematics, Springer, New York, 1985.
    • (1985) Lecture Notes in Mathematics , vol.1160
    • Van der Meer, J.C.1
  • 24
    • 0001459972 scopus 로고
    • Normal modes for nonlinear Hamiltonian systems
    • Weinstein A., Normal modes for nonlinear Hamiltonian systems. Invent. Math. 20:1973;47-57.
    • (1973) Invent. Math. , vol.20 , pp. 47-57
    • Weinstein, A.1
  • 25
    • 0032340303 scopus 로고    scopus 로고
    • The monodromy in the Hamiltonian Hopf bifurcation
    • Duistermaat J.J., The monodromy in the Hamiltonian Hopf bifurcation. Z. Angew. Math. Phys. 49:1998;156-161.
    • (1998) Z. Angew. Math. Phys. , vol.49 , pp. 156-161
    • Duistermaat, J.J.1
  • 26
    • 9344225119 scopus 로고    scopus 로고
    • A note on focus-focus singularities
    • Zung N.T., A note on focus-focus singularities. Diff. Geom. Appl. 7:1997;123-130.
    • (1997) Diff. Geom. Appl. , vol.7 , pp. 123-130
    • Zung, N.T.1
  • 27
    • 0010912802 scopus 로고
    • Points critiques des fonctions invariantes sur une G -varieté
    • Michel L., Points critiques des fonctions invariantes sur une. G -varieté C.R. Acad. Sci. Paris. 272:1971;433-436.
    • (1971) C.R. Acad. Sci. Paris , vol.272 , pp. 433-436
    • Michel, L.1
  • 30
    • 1542561309 scopus 로고    scopus 로고
    • On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family
    • Hanßmann H., van der Meer J.C., On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family. J. Dyn. Diff. Eqs. 14:2002;657-695.
    • (2002) J. Dyn. Diff. Eqs. , vol.14 , pp. 657-695
    • Hanßmann, H.1    Van Der Meer, J.C.2
  • 32
    • 18344372861 scopus 로고
    • Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. I. Physical picture and calculations
    • Du M., Delos J., Effect of closed classical orbits on quantum spectra: ionization of atoms in a magnetic field. I. Physical picture and calculations. Phys. Rev. A. 38:1988;1896-1912.
    • (1988) Phys. Rev. A , vol.38 , pp. 1896-1912
    • Du, M.1    Delos, J.2
  • 33
    • 24244464830 scopus 로고
    • Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. II. Derivation of formulas
    • Du M., Delos J., Effect of closed classical orbits on quantum spectra: ionization of atoms in a magnetic field. II. Derivation of formulas. Phys. Rev. A. 38:1988;1913-1930.
    • (1988) Phys. Rev. A , vol.38 , pp. 1913-1930
    • Du, M.1    Delos, J.2
  • 34
    • 0031187102 scopus 로고    scopus 로고
    • Quantum manifestations of bifurcations of closed orbits in the photoabsorption spectra of atoms in electric fields
    • Gao J., Delos J., Quantum manifestations of bifurcations of closed orbits in the photoabsorption spectra of atoms in electric fields. Phys. Rev. A. 56:1997;356-364.
    • (1997) Phys. Rev. A , vol.56 , pp. 356-364
    • Gao, J.1    Delos, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.