We study the collective association dynamics of a cold Fermi gas of 2N
atoms in M atomic modes into a single molecular bosonic mode. The many-body
fermionic problem for 2M amplitudes is effectively reduced to a dynamical
system of min{N,M}+1 amplitudes, making the solution no more complex than
the solution of a two-mode Bose-Einstein condensate and allowing realistic
calculations with up to 104 particles. The many-body dynamics is shown to be
formally similar to the dynamics of the bosonic system under the mapping of
boson particles to fermion holes, producing collective enhancement effects due
to many-particle constructive interference. Dissociation rates are shown to
enhance as the number of particles whereas association rates are enhanced as
the number of holes, leading to boson-like collective behavior.Comment: 5 pages, 2 figures, critical typo in Eq. (13) correcte