Adiabatic approximation, Gell-Mann and Low theorem, and degeneracies: A pedagogical example

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 4, 2008, Pages

  Brouder, Christian ^a   Stoltz, Gabriel ^a,b   Panati, Gianluca ^c  

^a INSTITUT DE PHYSIQUE DU GLOBE DE PARIS   (France)

^b INRIA   (France)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; HAMILTONIANS;

ADIABATIC; ADIABATIC APPROXIMATIONS; DEGENERATE CASES; EIGENSTATES; EVOLUTION OPERATORS; INITIAL STATES; QUANTUM STATES; SIMPLE SYSTEMS;

POLYNOMIAL APPROXIMATION;

EID: 54049096768     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.042102     Document Type: Article

References (17)

1. M. Gell-Mann and F. Low, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.84. 350 84, 350 (1951).
2. G. Nenciu and G. Rasche, Helv. Phys. Acta HPACAK 0018-0238 62, 372 (1989).
3. C. Bloch and J. Horowitz, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(58)90136-6 8, 91 (1958).
4. T. T. S. Kuo and E. Osnes, Folded-Diagram Theory of the Effective Interaction in Nuclei, Atoms and Molecules, Lecture Notes in Physics Vol. 364 (Springer-Verlag, Berlin, 1990).
5. D. M. Esterling and R. V. Lange, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.40.796 40, 796 (1968).
6. D. Mukherjee, Int. J. Quantum Chem., Quantum Chem. Symp. IJQSDI 0161-3642 10.1002/qua.560300737 S20, 409 (1986).
7. I. Lindgren, S. Salomonson, and B. Åsén, Phys. Rep. PRPLCM 0370-1573 390, 161 (2004).
8. P. J. Ellis and E. Osnes, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.49.777 49, 777 (1977).
9. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, Boston, 1971).
10. E. K. U. Gross, E. Runge, and O. Heinonen, Many-Particle Theory (Adam Hilger, Bristol, 1991).
11. M. Reed and B. Simon, Methods of Modern Mathematical Physics. II Fourier Analysis, Self-adjointness (Academic Press, New York, 1975).
12. E. Kamke, Differentialgleichungen: Bd.1, Gewöhnliche Differentialgleichungen, 6th ed. (Akademische Verlagsgesellschaft, Leipzig, 1959).
13. Handbook of Mathematical Functions, edited by, M. Abramowitz, and, I. Stegun, 5th ed. (Dover, New York, 1964).
14. T. Kato, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.5.435 5, 435 (1950).
15. A. Messiah, Mécanique Quantique (Dunod, Paris, 2003).
16. S. Teufel, Adiabatic Perturbation Theory in Quantum Dynamics, Lecture Notes in Mathematics Vol. 1821 (Springer, Berlin, 2003).
17. V. V. Tolmachev, in Correlation Effects in Atoms and Molecules, edited by, R. Lefebvre, and, C. Moser, Advances in Chemical Physics Vol. 14 (John Wiley, London, 1969), pp. 421-470.