 06265 A.P. Itin, A.A. Vasiliev$, and S. Watanabe
 Comment on "Nonlinear adiabatic passage from fermion atoms to
boson molecules"
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Sep 18, 06

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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 meanfield 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 meanfield 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
powerlaw $\Gamma \sim \alpha^{1/3}$ (in the case where the
initial fraction of molecules is larger than the quantum
fluctuations). Instead, $\Gamma$ is related to a quasirandom
jump of an adiabatic invariant which can be calculated using a
general method of the separatrix crossing theory and
asymptotically $\sim\alpha$ .
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