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A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys.Rev. Lett {\bf 120}, 040401 (2018)] measured for the first time the gradient ofthe Casimir force between two gold spheres in vacuum at room temperature, andplaced a bound on the magnitude of the deviation of the measured force from theproximity force approximation (PFA). The present work extends a previoustheoretical analysis of this experiment [G. Bimonte, Phys. Rev. D {\bf 97},085011 (2018)], by analyzing in detail how the magnitude of the deviation fromPFA is affected by the inclusion or neglect of ohmic dissipation at zerofrequency, a much debated issue in the current Casimir literature, which goesby the name of the Drude vs plasma controversy. We analyze as well the effectof connecting the plates to charge reservoirs, which is the standardconfiguration used in Casimir experiments. We describe a simple and effectivedecimation procedure, allowing for a faster computation of the Casimir forcefor large aspect ratios of the system.

physical review. d/physical review. d.

Beyond-proximity-force-approximation Casimir force between two spheres  at finite temperature II: plasma versus Drude modeling, grounded versus  isolated spheres