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Quasi-static protocols for systems that feature a mixed phase-space with bothchaos and quasi-regular regions are beyond the standard paradigm of adiabaticprocesses. We focus on a many-body system of atoms that are described by theBose-Hubbard Hamiltonian, specifically a circuit that consists of bosonicsites. We consider a sweep process: slow variation of the rotation frequency ofthe device (time dependent Sagnac phase). The parametric variation ofphase-space topology implies that the quasi-static limit is irreversible.Detailed analysis is essential in order to determine the outcome of suchtransfer protocol, and its efficiency.

Quasistatic transfer protocols for atomtronic superfluid circuits