  We study the heat transfer between N coupled quantum resonators with applied
synthetic electric and magnetic fields realized by changing the resonators
parameters by external drivings. To this end we develop two general methods,
based on the quantum optical master equation and on the Langevin equation for
$N$ coupled oscillators where all quantum oscillators can have their own heat
baths. The synthetic electric and magnetic fields are generated by a dynamical
modulation of the oscillator resonance with a given phase. Using Floquet theory
we solve the dynamical equations with both methods which allow us to determine
the heat flux spectra and the transferred power. With apply these methods to
study the specific case of a linear tight-binding chain of four quantum coupled
resonators. We find that in that case, in addition to a non-reciprocal heat
flux spectrum already predicted in previous investigations, the synthetic
fields induce here non-reciprocity in the total heat flux hence realizing a net
heat flux rectification.
