Abstract
In this review we discuss the chaotic dynamics (both classical and quantal aspects) of a simple atomic system, namely hydrogen atom interacting with time independent and time dependent external fields. These include: i) static electric field, ii) static magnetic field, iii) combined electric and magnetic fields, in parallel and perpendicular configuration, iv) instantaneous and generalized van der Waals field, v) mass anisotropy and vi) linearly and circularly polarized microwave fields.
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References
M Lakshmanan (ed.),Solitons—Introduction and Applications (Springer-Verlag, Berlin, 1988)
L E Reichl,The transition to chaos in conservative classical systems: Quantum manifestations (Springer-Verlag, Berlin, 1992)
A J Lichtenberg and M A Liberman,Regular and Stochastic Motion (Springer-Verlag, New York, 1983)
D Delande, in:Les Houches Session LII, Chaos and Quantum Physics 1989 edited by M-J Giannoni, A Voros and J Zinn-Justin (North Holland, Amsterdam, 1991)
F Haake,Quantum signatures of chaos (Springer, Berlin, 1991)
M C Gutzwiller,Chaos in classical and quantum mechanics (Springer-Verlag, New York, 1990)
R Ramaswamy and R A Marcus,J. Chem. Phys. 74, 1379 (1981);J. Chem. Phys. 74, 1385 (1981)
J E Howard,Phys. Rev. A51, 3934 (1995)
J Gao and J B Delos,Phys. Rev. A49, 869 (1994)
M Courtney, N Spellmeyer, H Jiao and D Kleppner,Phys. Rev. A51, 3604 (1995)
I Seipp and K T Taylor,J. Phys. B27, 2785 (1994)
I Seipp, K T Taylor and W Schweizer,J. Phys. B29, 1 (1996)
M Lakshmanan and K Ganesan,Curr. Sci. 68, 38 (1995)
T S Monteiro,Contemp. Phys. 35, 311 (1994)
J B Delos, S K Knudson and D W Noid,Phys. Rev. A30, 1208 (1984)
C Cohen Tannoudji, B Diu and F Laloe,Quantum Mechanics (Wiley, New York, 1977)
L D Landau, E M Lifshitz,Quantum mechanics—nonrelativistic theory (Pergamon Press, Oxford, 1965)
C W Clark and K T Taylor,J. Phys. B13, L737 (1980);J. Phys. B15, 1175 (1982);Nature 292, 437 (1982)
D Delande and A Buchleitner,Adv. At. Mol. Opt. Phys. 35, 85 (1994)
J Wals, H H Fielding, J F Christian, L C Snoek, W J van der Zande and H B van Linden van den Heuvell,Phys. Rev. Lett. 72, 3783 (1994)
H Fredrich and D Wintgen,Phys. Rep. 183, 37 (1989)
H Hasegawa, M Robnik and G Wunner,Prog. Theor. Phys. Suppl. 98, 198 (1989)
D R Herrick,Phys. Rev. A26, 323 (1982)
J B Delos, S K Knudson and D W Noid,Phys. Rev. A28, 7 (1983)
H Fredrich and M C Chu,Phys. Rev. A28, 1423 (1983)
W R S Garton and F S Tomkins,Astrophys. J. 158, 839 (1969)
A R P Rau,J. Phys. B12, L193 (1979)
C Iu, G R Welch, M M Kash, D Kleppner, D Delande and J C Gay,Phys. Rev. Lett. 66, 145 (1991)
K T Taylor, M H Nayfeh and C W Clark (eds),Physics of atoms and molecules: Atomic spectra and collisions in external fields (Plenum Press, London, 1988)
D Delande and J C Gay,Phys. Rev. Lett. 57, 2006 (1986)
G Wunner, U Woelk, I Zech, G Zeller, T Ertl, F Geyer, W Schweitzer and H Ruder,Phys. Rev. Lett. 57, 3261 (1986)
D Delande, A Bommier and J C Gay,Phys. Rev. Lett. 66, 141 (1991)
J Zakrzewski, K Dupret and D Delande,Phys. Rev. Lett. 74, 522 (1995)
K Dupret, J Zakrzewski and D Delande,Europhys. Lett. 31, 251 (1995)
P M Koch and K A H Van Leeuwen,Phys. Rep. 225, 289 (1995)
A D Peters, C Jaffe and J B Delos,Phys. Rev. Lett. 73, 2825 (1994)
M A Iken, F Borondo, R M Benito and T Uzer,Phys. Rev. A49, 2734 (1994)
P Cacciani, E Luc-koenig, J Pinard, C Thomas and S Liberman,Phys. Rev. Lett. 56, 1467 (1986)
H H Fielding, J Wals, W J van der Zande and H B van Linden van den Heuvell,Phys. Rev. A51, 611 (1995)
J M Amo, K A Rapelje, S J Blodgett-Ford, J B Delos, A Konig and H Rinneberg,Phys. Rev. A48, 2117 (1993)
K Richter, D Wintgen and J S Briggs,J. Phys. B20, L627 (1987)
K T Taylor, W S Schweizer, M A Al-Laithy, P F O’Mahony, S Bivone and C M Farmer, in:Classical dynamics in atomic and molecular physics (World Scientific, Singapore, 1989)
M Courtney,Phys. Rev. A51, 4558 (1995)
P Fassbinder and W Schweizer,Phys. Rev. A53, 2135 (1996)
Jan von Milczewski, G H F Diercksen and T Uzer,Phys. Rev. Lett. 76, 2890 (1996)
G Raithel, M Fauth and H Walther,Phys. Rev. A44, 1898 (1991)
T Uzer and D Farrelly,Phys. Rev. A52, R2501 (1995)
G Raithel and H Walther,Phys. Rev. A49, 1646 (1994)
G C Hegerfeldt and R Henneberg,Phys. Rev. A49, 3531 (1994)
Jan von Milczewski, G H F Diercksen and T Uzer,Phys. Rev. Lett. 73, 2428 (1994)
J Main and G Wunner,J. Phys. B27, 2835 (1994)
K Ganesan and K T Taylor,J. Phys. B29, 1293 (1996)
V S Melezhik,Phys. Rev. A52, R3393 (1995)
K Ganesan and M Lakshmanan,Phys. Rev. Lett. 62, 232 (1989);Phys. Rev. A42, 3940 (1990);Phys. Rev. A45, 1548 91992);Phys. Rev. A48, 964 (1993);J. Phys. B27, 2809 (1994)
J E Howard and D Farrelly,Phys. Lett. A178, 62 (1993)
D Farrelly and J E Howard,Phys. Rev. A48, 851 (1993)
G Baumann and T F Nonnenmacher,Phys. Rev. A46, 2682 (1992)
M Lakshmanan and K Ganesan,J. Phys. Soc. Jpn. Suppl. A63, 47 (1994)
R Blümel, C Kappler, W Quint and H Walther,Phys. Rev. A40, 808 (1989)
R A Faulkner,Phys. Rev. 184, 713 (1969)
D Wintgen and H Marxer,Phys. Rev. Lett. 60, 971 (1988)
M C Gutzwiller,Physica D5, 183 (1992)
D Wintgen, H Marxer and J S Briggs,J. Phys. A20, L965 (1987)
André Bandrauk (ed.),Atoms and molecular processes with short intense laser pulses, NATO ASI Series B: Physics (Plenum Press, New York, 1988) vol. 171
J E Bayfield and P M Koch,Phys. Rev. Lett. 33, 258 (1974)
T F Gallagher,Mod. Phys. Lett. B5, 259 (1991)
M Gatzke, B Broers, L D Noordam, R B Watkins and T Gallagher,Phys. Rev. A50, 2502 (1994)
R Blümel, A Buchleitner, R Graham, L Sirko, U Smilansky and H Walther,Phys. Rev. A44, 4521 (1991)
M W Bellermann, P M Koch, D R Mariani and D Richards,Phys. Rev. Lett. 76, 892 (1996)
P Fu, T J Scholz, J M Hettema and T F Gallagher,Phys. Rev. Lett. 64, 511 (1990)
J G Leopold and I C Percival,Phys. Rev. Lett. 41, 944 (1978)
D Banks and J G Leopold,J. Phys. B11, 37 (1978)
J G Leopold and I C Percival,J. Phys. B12, 709 (1979)
N B Delone, B A Zon and V P Krainov,Zh. Eksp. Teor. Fiz. 75, 445 (1978); [Sov. Phys. JETP 48, 223 (1978)]
B I Meerson, E A Oks and P V Sasorov,Pisma Zh. Eksp. Teor. Fiz. 29, 79 (1979); [Sov. Phys. JETP Lett. 29, 72 (1979)]
K Burnett, V C Reed and P L Knight,J. Phys. B26, 561 (1993)
A O Barut, C K E Schneider and R Wilson,J. Math. Phys. 20, 2244 (1979)
A C Chen,Phys. Rev. A22, 333 (1980);23, 1655 (1981)
R Gębarowski and J Zakrzewski,Phys. Rev. A51, 1508 (1995)
M Gajda, J Grochmalicki, M Lewenstein and K Rzążewski,Phys. Rev. A46, 1638 (1992)
R S MacKay, J D Meiss and I C Percival,Phys. Rev. Lett. 52, 697 (1984)
J D Meiss,Phys. Rev. Lett. 62, 1576 (1989)
C F Hillermeier, R Blümel and U Smilansky,Phys. Rev. A45, 3486 (1992)
Y-C Lai, C Grebogi, R Blümel and M Ding,Phys. Rev. A45, 8284 (1992)
J E Bayfield, S Y Luie, L C Perotti and M P Skrzypkowski,PHys. Rev. A53, R12 (1996)
R Gębarowski and J Zakrzewski,Phys. Rev. A50, 4408 (1994)
A Buchleitner, D Delande, J Zakrzewski, R N Mantegna, M Arndt and H Walther,Phys. Rev. Lett. 75, 3818 (1995)
K Kulander, K J Schafer and J L Krause,Phys. Rev. Lett. 66, 2601 (1991)
J L Krause, K J Schafer and K Kulander,Phys. Rev. A45, 4998 (1992)
J Parker, K T Taylor, C W Clark and S Blodgett-Ford,J. Phys. B29, L33–42 (1996)
J H Shirley,Phys. Rev. B138, 979 (1965)
S-I Chu and W P Reinhardt,Phys. Rev. Lett. 39, 1195 (1977)
A Buchleitner, D Delande and J-C Gay,J. Opt. Soc. Am. B12, 505 (1995)
J Zakrzewski, D Delande, J C Gay and K Rzążewski, Phys. Rev.A47, R2468 (1993)
B V Chirikov,Phys. Rep. 52, 263 (1979)
M V Berry and K E Mount,Rep. Prog. Phys. 35, 315 (1972)
C D Schwieters and J B Delos,Phys. Rev. A51, 1023 (1995)
F Benvenuto, G Casati and D L Shepelyansky,Phys. Rev. A45, R7670 (1992);Phys. Rev. A47, R786 (1993)
G Casati, I Guarneri and D L Shepelyansky,IEEE J. Quant. Electron. 24, 1240 (1988)
M Wójcik, J Zakrzewski and K Rzążewski,Phys. Rev. A52, R2523 (1995)
J Zakrzewski and K Życzkowski,Phys. Rev. A36, 4311 (1987)
D Wintgen,Z. Phys. D18, 125 (1991)
M J Raković and S-I Chu,Phys. Rev. A50, 5077 (1994)
K Rzążewski and B Piraux,Phys. Rev. A47, R1612 (1993)
J Mostowski and J J Sanchez-Mondragon,Opt. Commun. 29, 293 (1979)
B I Meerson, E A Oks and P V Sasorov,J. Phys. B15, 3599 (1982)
J Zakrzewski, R Gębarowski and D Delande,Phys. Rev. A54, 691 (1996)
M Nauenberg,Europhys. Lett. 13, 611 (1990)
J E Howard,Phys. Rev. A46, 364 (1992)
P Kappertz and M Nauenberg,Phys. Rev. A47, 4749 (1993)
D Farrelly and T Uzer,Phys. Rev. Lett. 74, 1720 (1995)
I Białynicki-Birula, M Kaliński and J H Eberly,Phys. Rev. Lett. 73, 1777 (1994)
M Kaliński, J H Eberly and I Białynicki-Birula,Phys. Rev. A52, 2460 (1995)
D Delande, J Zakrzewski and A Buchleitner,Europhys. Lett. 32, 107 (1995)
J Zakrzewski, D Delande and A Buchleitner,Phys. Rev. Lett. 75, 4015 (1995)
G Casati, B V Chirikov, D L Shepelyansky and I Guarneri,Phys. Rep. 154, 77 (1987)
S Benkadda, Y Elskens, B Ragot and J T Mendonça,Phys. Rev. Lett. 72, 2859 (1994)
R Blümel and U Smilansky,Z. Phys. D6, 83 (1987)
G Hose and H S Taylor,Phys. Rev. Lett. 51, 947 (1983)
J Zakrzewski, D Delande and M Kuś,Phys. Rev. E47, 1665 (1993)
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Ganesan, K., Gębarowski, R. Chaos in the hydrogen atom interacting with external fields. Pramana - J Phys 48, 379–410 (1997). https://doi.org/10.1007/BF02845652
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DOI: https://doi.org/10.1007/BF02845652
Keywords
- Classical and quantum chaos
- hydrogen atom in external fields
- Stark and Zeeman effect
- van der Waals field
- linearly and circularly polarized microwave
- ionization
- diffusion
- Rydberg states