Work exchange, geometric magnetization, and fluctuation-dissipation relations in a quantum dot under adiabatic magnetoelectric driving

We study the adiabatic dynamics of the charge, spin, and energy of a quantum dot with a Coulomb interaction under two-parameter driving, associated to time-dependent gate voltage and magnetic field. The quantum dot is coupled to a single reservoir at temperature T = 0 and the dynamical Onsager matrix is fully symmetric, hence, the net energy dynamics is fully dissipative. However, in the presence of many-body interactions, other interesting mechanisms take place, like the net exchange of work between the two types of forces and the nonequilibrium accumulation of charge with different spin orientations. The latter has a geometric nature. The dissipation takes place in the form of an instantaneous Joule law with the universal resistance R-0 = h/2e(2). We show the relation between this Joule law and instantaneous fluctuation-dissipation relations. The latter lead to generalized Korringa-Shiba relations, valid in the Fermi-liquid regime.