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Quantum averaging and resonances: Two-level atom in a one-mode quantized field
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10.1063/1.1864252
/content/aip/journal/jmp/46/4/10.1063/1.1864252
http://aip.metastore.ingenta.com/content/aip/journal/jmp/46/4/10.1063/1.1864252
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Figures

Image of FIG. 1.
FIG. 1.

Comparison of exact numerical eigenvalues (dashed lines) of (8) for one-photon resonance with the approximate ones (solid lines) obtained after (a) one one-photon RT given by (34) and (b) one one-photon RT plus one iteration of KAM-type perturbative expansion. The divergence observed around in panel (b) is due to the active nonlinear resonances of that occurred at the degeneracies marked by circles in panel (a). One can see clearly that the locations of these resonances depend on according to Eq. (35).

Image of FIG. 2.
FIG. 2.

Comparison of the exact numerical eigenvalues (dashed lines) of (8) for one-photon resonance with the approximate ones (solid lines) obtained respectively after (a) one one-photon RT given by (34), (b) one one-photon RT plus one two-photon RTs given by (49), (c) one one-photon RT plus two two-photon RTs, (d) one one-photon RT plus three two-photon RTs, (e) one one-photon RT plus four two-photon RTs, (f) one one-photon RT plus four two-photon RTs plus one iteration of KAM-type perturbative expansion. The divergence of the KAM transformation observed close to in panel (f) is due to the presence of active resonances at larger values of .

Image of FIG. 3.
FIG. 3.

Comparison of exact numerical eigenvalues (dashed lines) of (8) as a function of the coupling constant in the resonant case , with the approximate eigenvalues (solid lines) obtained from (65).

Image of FIG. 4.
FIG. 4.

Comparison of exact numerical spectrum of (8) (dashed lines) as a function of the coupling constant in the resonant case , with the quite accurate result (75) which has treated the zero-field resonances by a RT (solid lines).

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/content/aip/journal/jmp/46/4/10.1063/1.1864252
2005-03-30
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum averaging and resonances: Two-level atom in a one-mode quantized field
http://aip.metastore.ingenta.com/content/aip/journal/jmp/46/4/10.1063/1.1864252
10.1063/1.1864252
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