Mesoscopic capacitor and zero-point energy: Poisson's distribution for virtual charges, pressure, and decoherence control

Mesoscopic capacitor theory, which includes intrinsic inductive effects from quantum tunneling, is applied to conducting spherical shells. The zero-point pressure and the number of virtual charged pairs are determined assuming a Poisson distribution. They are completely defined by a dimensionless mesoscopic parameter (χ_c) measuring the average number of virtual pairs per solid angle and carrying mesoscopic information. Fluctuations remain finite and well defined. Connections with usual quantum-field-theory limit enables us to evaluate χ_c ∼ 1.007110. Equivalently, for a mesoscopic parallel-plate capacitor, the shot noise distribution becomes operative with χ_c ∼ 0.94705 as well being related to the density of virtual pairs. Temperature decoherence and capacitor control are discussed by considering typical values of quantum dot devices and Coulomb blockade theory.