메뉴 건너뛰기




Volumn 35, Issue 8, 2010, Pages 1490-1515

Passage from quantum to classical molecular dynamics in the presence of Coulomb Interactions

Author keywords

Liouville equation; Quantum dynamics; Singular potentials; Wigner transformation

Indexed keywords


EID: 77954269399     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605301003657835     Document Type: Article
Times cited : (16)

References (33)
  • 1
    • 7544243351 scopus 로고    scopus 로고
    • Transport equation and Cauchy problem for BV vector fields
    • Ambrosio, L. (2004). Transport equation and Cauchy problem for BV vector fields. Invent. Math. 158:227-260.
    • (2004) Invent. Math , vol.158 , pp. 227-260
    • Ambrosio, L.1
  • 4
    • 84904278040 scopus 로고    scopus 로고
    • Equations de transport à coefficient dont le gradient est donné par une intégrale singulière [Equations of transport coefficient when the gradient is given by a singular integral]
    • Palaiseau, France: École Polytechnique
    • Bouchut, F., Crippa, G. (2009). Equations de transport à coefficient dont le gradient est donné par une intégrale singulière [Equations of transport coefficient when the gradient is given by a singular integral]. Sèminaire Èquations aux Dèrivèes Partielles. Palaiseau, France: École Polytechnique.
    • (2009) Sèminaire Èquations Aux Dèrivèes Partielles
    • Bouchut, F.1    Crippa, G.2
  • 6
    • 1642394833 scopus 로고    scopus 로고
    • The level crossing problem in semi-classical analysis I, the symmetric case
    • Colin de Verdiére, Y. (2003). The level crossing problem in semi-classical analysis I, the symmetric case. Ann. Inst. Fourier 53:1023-1054.
    • (2003) Ann. Inst. Fourier , vol.53 , pp. 1023-1054
    • Colin de Verdiére, Y.1
  • 7
    • 0038391347 scopus 로고    scopus 로고
    • Une formule de Landau-Zener pour un croisement non dégénéré et involutif de codimension 3
    • Fermanian-Kammerer, C., Gérard, P. (2002). Une formule de Landau-Zener pour un croisement non dégénéré et involutif de codimension 3 [A Landau-Zener formula for a non-degenerate and involutive crossing of codimension 3]. C. R. Acad. Sci. Paris, Ser. I 335:915-920.
    • (2002) C. R. Acad. Sci. Paris, Ser , vol.1 , Issue.335 , pp. 915-920
    • Fermanian-Kammerer, C.1    Gérard, P.2
  • 8
    • 0037324071 scopus 로고    scopus 로고
    • Wigner measures and codimension two crossings
    • Fermanian-Kammerer, C., Lasser, C. (2003). Wigner measures and codimension two crossings. J. Math. Phys. 44:507-527.
    • (2003) J. Math. Phys , vol.44 , pp. 507-527
    • Fermanian-Kammerer, C.1    Lasser, C.2
  • 9
    • 0042977329 scopus 로고    scopus 로고
    • The multiconfiguration equations for atoms and molecules: Charge quantization and existence of solutions
    • Friesecke, G. (2003). The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions. Arch. Rat. Mech. Analysis 169:35-71.
    • (2003) Arch. Rat. Mech. Analysis , vol.169 , pp. 35-71
    • Friesecke, G.1
  • 10
    • 77954275990 scopus 로고    scopus 로고
    • Monograph in preparation
    • Friesecke, G. Monograph in preparation.
    • Friesecke, G.1
  • 12
    • 0001342333 scopus 로고
    • Microlocal defect measures
    • Gérard, P. (1991). Microlocal defect measures. Comm. Part. Diff. Eqs. 16: 1761-1794.
    • (1991) Comm. Part. Diff. Eqs , vol.16 , pp. 1761-1794
    • Gérard, P.1
  • 13
    • 21844435003 scopus 로고
    • Collisions for the quantum Coulomb Hamiltonian
    • Gérard, C., Knauf, A. (1991). Collisions for the quantum Coulomb Hamiltonian. Comm. Math. Phys. 143:17-26.
    • (1991) Comm. Math. Phys , vol.143 , pp. 17-26
    • Gérard, C.1    Knauf, A.2
  • 15
    • 0001118605 scopus 로고
    • Molecular Propagation through Electron Energy Level Crossings
    • Providence, RI: American Mathematical Society
    • Hagedorn, G. (1994). Molecular Propagation through Electron Energy Level Crossings. Memoirs AMS, Vol. 536. Providence, RI: American Mathematical Society.
    • (1994) Memoirs AMS , vol.536
    • Hagedorn, G.1
  • 16
    • 0000371221 scopus 로고
    • Distortion analyticity and molecular resonance curves
    • Hunziker, W. (1986). Distortion analyticity and molecular resonance curves. Ann. Inst. H. Poincaré Phys. Théor. 45:339-358.
    • (1986) Ann. Inst. H. Poincaré Phys. Théor , vol.45 , pp. 339-358
    • Hunziker, W.1
  • 17
    • 84966238625 scopus 로고
    • Fundamental properties of Hamiltonian operators of Schrödinger type
    • Kato, T. (1951). Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. AMS 70:195-211.
    • (1951) Trans. AMS , vol.70 , pp. 195-211
    • Kato, T.1
  • 19
    • 21844450863 scopus 로고    scopus 로고
    • Wigner measure dynamics in a Coulomb potential
    • 063512
    • Keraani, S. (2005). Wigner measure dynamics in a Coulomb potential. J. Math. Phys. 46:063512, 21 pp.
    • (2005) J. Math. Phys , vol.46 , pp. 21
    • Keraani, S.1
  • 21
    • 25444450804 scopus 로고    scopus 로고
    • Propagation through conical crossings: An asymptotic transport equation and numerical experiments
    • Lasser, C., Teufel, S. (2005). Propagation through conical crossings: an asymptotic transport equation and numerical experiments. Comm. Pure Appl. Math. 58:1188-1230.
    • (2005) Comm. Pure Appl. Math , vol.58 , pp. 1188-1230
    • Lasser, C.1    Teufel, S.2
  • 23
    • 0001314058 scopus 로고
    • Sur les mesures de Wigner
    • Lions, P.-L., Paul, T. (1993). Sur les mesures de Wigner [On Wigner measures]. Rev. Mat. Iberoamericana 9:553-618.
    • (1993) Rev. Mat. Iberoamericana , vol.9 , pp. 553-618
    • Lions, P.-L.1    Paul, T.2
  • 24
    • 84988209878 scopus 로고
    • On the equivalence of the Schrödinger and the quantum Liouville equations
    • Markowich, P.A. (1989). On the equivalence of the Schrödinger and the quantum Liouville equations. Math. Meth. Appl. Sci. 11:459-469.
    • (1989) Math. Meth. Appl. Sci , vol.11 , pp. 459-469
    • Markowich, P.A.1
  • 26
    • 0000424988 scopus 로고
    • Uber das verhalten von eigenwerten bei adiabatischen prozessen
    • Neumann, J.v., Wigner, E. (1929). Uber das verhalten von eigenwerten bei adiabatischen prozessen [On the behavior of eigenvalues at adiabatic processes]. Physik. Zeitschr. 30:467-470.
    • (1929) Physik. Zeitschr , vol.30 , pp. 467-470
    • Neumann, J.V.1    Wigner, E.2
  • 30
    • 84974050752 scopus 로고
    • H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
    • Tartar, L. (1992). H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 115:193-230.
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , pp. 193-230
    • Tartar, L.1
  • 31
    • 0344940075 scopus 로고    scopus 로고
    • Adiabatic Perturbation Theory in Quantum Dynamics
    • Berlin: Springer-Verlag
    • Teufel, S. (2003). Adiabatic Perturbation Theory in Quantum Dynamics. Lecture Notes in Mathematics, vol. 1821. Berlin: Springer-Verlag.
    • (2003) Lecture Notes In Mathematics , vol.1821
    • Teufel, S.1
  • 32
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • Wigner, E. (1932). On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40:749-759.
    • (1932) Phys. Rev , vol.40 , pp. 749-759
    • Wigner, E.1
  • 33
    • 0001332554 scopus 로고
    • Non-adiabatic crossing of energy levels
    • Zener, C. (1932). Non-adiabatic crossing of energy levels. Proc. R. Soc. London, Ser. A 137:696-702.
    • (1932) Proc. R. Soc. London, Ser. A , vol.137 , pp. 696-702
    • Zener, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.