Quantum oscillations order in boson+fermion dimer models

We study the quantum oscillations for the cuprate superconductors in the underdoped pseudogap regime. We represent the system as a fermion+boson dimer model. We reduce the problem to an effective problem of free fermions hopping in an external field (which is not identical to a static magnetic field). We find the semiclassical equations of motion for these fermions. We find that the dimers undergo quantum oscillations in a strong magnetic field with the oscillation magnitude obeying the Lifshitz Kosevich formula.