Difference between the vacuum Casimir energies for grounded and isolated conductors

FOSCO, C.D.; MAZZITELLI, F.D.; LOMBARDO, F.C.

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Lugar: New York; Año: 2016 vol. 94 p. 850241 - 850247

0556-2821

We study the vacuum (i.e., zero-temperature) Casimir energy for a system of neutral conductors which are isolated, as opposed to grounded. The former is meant to describe a situation where the total charge on each conductor, as well as all of its fluctuations, vanishes, while the latter describes a situation where the conductors are connected to a charge reservoir. We compute the difference between the vacuum energies for a given system of conductors, but subjected to the two different conditions stated above. The results can be written in terms of a generalized, frequency-dependent capacitance matrix of the system. Using a multipolar expansion, we show that the grounded Casimir energy includes a monopole-monopole interaction term that is absent in the isolated case in the large distance limit.