Abstract
In this work a nonlinear evolution of pure states of a finite dimensional quantum system is introduced, in particular a Riccati evolution equation. It is shown how this class of dynamics is actually a Hamiltonian dynamics in the complex projective space. In this projective space it is shown that there is a nonlinear superposition rule, consistent with its linear counterpart in the Hilbert space. As an example, the developed nonlinear formalism is applied to the semiclassical Jaynes–Cummings model.
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