The Casimir force between rough metallic plates
نویسندگان
چکیده
– The Casimir force between two metallic plates is affected by their roughness state. This effect is usually calculated through the so-called 'proximity force approximation' which is only valid for small enough wavevectors in the spectrum of the roughness profile. We introduce here a more general description with a wavevector-dependent roughness sensitivity of the Casimir effect. Since the proximity force approximation underestimates the effect, a measurement of the roughness spectrum is needed to achieve the desired level of accuracy in the theory-experiment comparison. Introduction. – The Casimir force [1] has recently been measured with a good experimental precision which allows for an accurate comparison between measured values and theoretical predictions [2, 3]. This comparison plays an important role in the searches of new weak forces with nanometric to millimetric ranges motivated by theoretical unification models [4, 5, 6]. These forces would appear as experiment/theory differences in precise measurements of the Casimir force. As far as an accurate theory-experiment comparison is aimed at, the accuracy of theory is as crucial as the precision of experiments. If the target is a given accuracy, say at the 1% level, the theoretical prediction has to be mastered at this level as well as the experimental measurement. Clearly, this requires to take into account the real conditions of the experiments which differ from the ideal situation often assumed in the theory of the Casimir effect. Casimir initially studied the case of a pair of perfectly smooth, flat and parallel plates in the limit of zero temperature and perfect reflection. He found a force which depends only on geometrical properties, the distance L between the plates and their area A supposed to be much larger than L 2 , and two fundamental constants, c and. This remarkable fact is related to the assumption of perfect reflection while the most precise experiments [7, 8] are performed with metallic mirrors which are nearly perfect reflectors only at frequencies smaller than a characteristic plasma frequency ω P. It follows that the theoretical expectation of
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