We study the tunneling of a spin polarized Fermi gas in a three-dimensional
double well potential, focusing on the time dynamics starting from an initial
state in which there is an imbalance in the number of particles in the two
wells. Although fermions in different doublets of the double well tunnel with
different frequencies, we point out that (incoherent) oscillations of a large
number of particles can arise, as a consequence of the presence of transverse
degrees of freedom. Estimates of the doublet structure and of the occupation of
transverse eigenstates for a realistic experimental setup are provided.Comment: 10 pages, Typos corrected and figures changed - published in Laser
Physics, issue on the LPHYS'11 conference (Sarajevo, 2011