**
Below is the ascii version of the abstract for 06-265.
The html version should be ready soon.**A.P. Itin, A.A. Vasiliev$, and S. Watanabe
Comment on "Nonlinear adiabatic passage from fermion atoms to
boson molecules"
(710K, Ps)
ABSTRACT. Dynamics of an adiabatic sweep through a Feshbach resonance in a
quantum gas of fermionic atoms was considered recently in
I.Tikhonenkov, E.Pazy {\it et al}, Phys. Rev. {\bf A 73}, 043605
(2006). In the mean-field limit, the system is reduced to a
classical nonlinear Hamiltonian system with a slowly changing
parameter. Analysis of the latter system was done incorrectly; the
main results of the commented paper are inconsistent. Here we
present accurate study of the mean-field dynamics of the model
based on the rigorous separatrix crossing theory. In particular,
for the dependence of the remaining atomic fraction $\Gamma$ on
the sweep rate $\alpha$ the abovementioned Refs. predict the
power-law $\Gamma \sim \alpha^{1/3}$ (in the case where the
initial fraction of molecules is larger than the quantum
fluctuations). Instead, $\Gamma$ is related to a quasi-random
jump of an adiabatic invariant which can be calculated using a
general method of the separatrix crossing theory and
asymptotically $\sim\alpha$ .