# Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories

## TL;DR

This paper introduces a quantum mixing approach based on Time-Dependent Hartree-Fock Bogolyubov trajectories to accurately describe particle transfer in superfluid systems with restored particle number symmetry, improving upon previous qualitative models.

## Contribution

The paper presents a simplified Multi-Configuration TDHFB method that effectively restores particle number symmetry in dynamical superfluid systems, matching exact solutions across various conditions.

## Key findings

- Excellent agreement with exact solutions for symmetric and asymmetric superfluid systems.
- Effective in weak to strong interaction regimes.
- Highlights benefits and limitations for realistic system applications.

## Abstract

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.