Quantum interference phenomena in the Casimir effect

We propose a definitive test of whether plates involved in Casimir experiments should be modeled with ballistic or diffusive electrons—a prominent controversy highlighted by a number of conflicting experiments. The unambiguous test we propose is a measurement of the Casimir force between a disordered quasi-two-dimensional metallic plate and a three-dimensional metallic system at low temperatures, in which disorder-induced weak-localization effects modify the well-known Drude result in an experimentally tunable way. We calculate the weak-localization correction to the Casimir force as a function of magnetic field and temperature and demonstrate that the quantum interference suppression of the Casimir force is a strong, observable effect. The coexistence of weak-localization suppression in electronic transport and Casimir pressure would lend credence to the Drude theory of the Casimir effect, while the lack of such correlation would indicate a fundamental problem with the existing theory. We also study mesoscopic disorder fluctuations in the Casimir effect and estimate the width of the distribution of Casmir energies due to disorder fluctuations