Noncontact gears. II. Casimir torque between concentric corrugated cylinders for the scalar case

Abstract

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for non-contact gears. To this end, we calculate the Casimir torque between two such cylinders, described by δ-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed. * Electronic address: Ines.Cavero-Pelaez@spectro.jussieu.fr † Electronic address: milton@nhn.ou.edu; URL: http://www.nhn.ou.edu/%7Emilton ‡ Electronic address: prachi@nhn.ou.edu § Electronic address: shajesh@nhn.ou.edu; URL: http://www.nhn.ou.edu/%7Eshajesh

Casimir torque between nanostructured plates

“…In this case a vacuum induced Casimir torque arises, which is the main issue of the present paper. Interesting perspectives for Casimir torques lie in the design of noncontact gears [25,26] which would allow for torque transmission between two nanostructured plates avoiding any direct contact between them. As the rotational symmetry is broken in this case, the Casimir torque arises because the Casimir energy now depends on the angle θ between the two directions of the corrugations.…”

Many-body contributions to Green’s functions and Casimir energies

“…(2) can be controlled. This has now been demonstrated by explicit calculations for a number of geometries and physical situations [18][19][20][21].…”

Casimir torque between two inhomogeneous semi-transparent concentric cylinders

“…[6,17,18,19]). In addition, the strategy of computing the Casimir torque for corrugated cylinders is discussed by Cavero-Pleaez in [6].…”

“…[6,17,18,19]). In addition, the strategy of computing the Casimir torque for corrugated cylinders is discussed by Cavero-Pleaez in [6]. Generalizing this approach, in this paper, in order to compute the Casimir torque between two concentric cylinders, we try to investigate an idea based on using inhomogeneous surfaces instead of corrugated ones which can be one of the interesting aspects of Casimir phenomena [20].…”

“…For these configurations one may consider the angular analogue of the Casimir force, the Casimir torque, which is its other important aspect and plays a major role in the recently developed nano-motors idea that was first proposed in [4]. The torque between two corrugated conducting plates and also for concentric corrugated conducting cylinders for the scalar field was calculated after that [5,6,7].…”