NONTRIVIAL DYNAMICS INDUCED BY A NONLINEAR JAYNES-CUMMINGS HAMILTONIAN

The addition of a nonlinear term to the Jaynes-Cummings Hamiltonian in duced a nontrivial discrete dynamics for the number of possible transi tions of a given order, represented by a Fibonacci series. We describe the physics of the problem in terms of relevant operators which close a semi-Lie algebra under commutation with the Hamiltonian and therefo re extending the generalized Bloch equations, already obtained for the linear case, to the nonlinear one. The initial conditions as well as a thermodynamical treatment of the problem is analyzed via the maximum entropy principle density operator. Finally, a generalized solution f or the time-independent case is obtained and the solution for the fiel d in a thermal state is recovered.