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 $\sim\alpha$ .