  While superfluidity is accurately grasped with a state that explicitly breaks
the particle number symmetry, a precise description of phenomena like the
particle transfer during heavy-ion reactions can only be achieved by
considering systems with good particle numbers. We investigate the possibility
to restore particle number in many-body dynamical problems by mixing-up several
Time-Dependent Hartree-Fock Bogolyubov (TDHFB) trajectories. In our approach,
each trajectory is independent from the others and the quantum mixing between
trajectories is deduced from a variational principle. The associated theory can
be seen as a simplified version of the Multi-Configuration TDHFB (MC-TDHFB)
theory. Its accuracy to tackle the problem of symmetry restoration in dynamical
problems is illustrated for the case of two superfluid systems that exchange
particles during a short time. In Ref. [Phys. Rev. C 97, 034627 (2018)], using
a schematic model where two systems initially described by a pairing
Hamiltonians are coupled during a short contact time, it was demonstrated that
statistical mixing of TDHFB trajectories can only qualitatively describe the
transfer process and that a fully quantum treatment is mandatory. We show here
that the present MC-TDHFB approach gives an excellent agreement with the exact
solution when the two superfluids are the same (symmetric case) or different
(asymmetric case) and from weak to strong interaction strength. Finally, we
discuss the benefits and bottleneck of this method in view of its application
to realistic systems.
