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Even-odd anomalous tunneling effect.

The analysis of the interacting fermion models with the SU(2) symmetry indicates the different behavior of the splittings of opposite-parity lowest-energy eigenstates for even and odd numbers of fermions. The imaginary time-dependent mean-field approach reproduces the average results only. For the odd particle numbers, an introduction of the universal logarithmic term to the action integral is needed. The even-odd effect appears in a wide class of models with the SU(2) symmetry and is connected with the crossing of the energy surfaces of opposite-parity states for an odd number of fermions.