Non-integrability of the semiclassical Jaynes--Cummings models without the rotating-wave approximation

摘要

Two versions of the semi-classical Jaynes--Cummings model without therotating wave approximation are investigated. It is shown that for a non-zerovalue of the coupling constant the version introduced by Belobrov, Zaslavsky,and Tartakovsky is Hamiltonian with respect to a certain degenerated Poissonbracket. Moreover, it is shown that both models are not integrable.