Casimir force between eccentric cylinders

PACS. 03.70.+k – Theory of quantized fields. PACS. 42.50.Pq – Cavity quantum electrodynamics; micromasers. PACS. 04.80.Cc – Experimental tests of gravitational theories. Abstract. – We consider the Casimir interaction between a cylinder and a hollow cylin-der, both conducting, with parallel axis and slightly different radii. The Casimir force, which vanishes in the coaxial situation, is evaluated for both small and large eccentricities using the proximity approximation. The cylindrical configuration offers various experimental advantages with respect to the parallel planes or the plane-sphere geometries, leading to favourable condi-tions for the search of extra-gravitational forces in the micrometer range and for the observation of finite-temperature corrections. Casimir forces are one of the most striking macroscopic manifestations of vacuum quantum fluctuations. Recently, there has been an increasing interest in experimental and theoretical aspects of these forces [1]. The force between parallel conducting plates as originally predicted in [2], after a first evidence reported in [3], has recently been measured at the 15 % accuracy level using cantilevers [4]. A force of similar nature between a conducting plane and a conduct