Artur Ishkhanyan et al 2005 J. Phys. A: Math. Gen. 38 3505 doi:10.1088/0305-4470/38/16/003
Artur Ishkhanyan1,3, Juha Javanainen2 and Hiroki Nakamura3
Show affiliationsA basic nonlinear two-state model generic in classical and bosonic field theories with a cubic nonlinearity is considered. For the class of models with constant external field amplitude a general strategy for attacking the problem is developed based on the reduction of the initial system of equations for the semi-classical atom–molecule amplitudes to a nonlinear Volterra integral equation for the molecular probability. A uniformly convergent series solution to the problem is constructed for the weak interaction limit. The Landau–Zener model is considered as a specific example. The first approximation term is derived and an asymptotic expression for the nonlinear transition probability is established in the weak interaction regime.
Issue 16 (22 April 2005)
Received 1 July 2004, in final form 18 January 2005
Published 6 April 2005
Artur Ishkhanyan et al 2005 J. Phys. A: Math. Gen. 38 3505
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