Exploring the quantum vacuum with cylinders

Abstract

We review recent work on the Casimir interaction energy between cylindrical shells. We include proposals for future experiments involving cylinders, such us a null experiment using quasi-concentric cylinders, a cylinder in front a conducting plate, and a cylindrical version of the rack and pinion powered by Casimir lateral force. We also present an exact formula for the theoretical evaluation of the vacuum interaction energy between eccentric cylindrical shells, and describe improved analytical and numerical evaluations for the particular case of concentric cylinders.

Casimir interaction between two concentric cylinders at nonzero temperature

“…This agrees with the result obtained in [31]. On the other hand, the high temperature asymptotic expansion is…”

“…The zero temperature Casimir interaction between two concentric cylinders has been considered in [28][29][30][31][32][33]. Here we consider the finite temperature correction.…”

“…Let d = a 2 − a 1 be the separation between the cylinders. At zero temperature, the Casimir interaction energy between the two cylinders is given by * Electronic address: LeePeng.Teo@nottingham.edu.my [ [30][31][32][33]:…”

Casimir torque between two inhomogeneous semi-transparent concentric cylinders

“…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].…”

Casimir interaction between spherical and planar plasma sheets

“…In the case that the objects have certain symmetries that allow a separable coordinate system to be employed, one can calculate these matrices explicitly. This has made possible the exact analytic and numerical analysis of the Casimir interaction between a sphere and a plate [18][19][20][21][22][23][24][25][26][27][28][29], between two spheres [30][31][32], between a cylinder and a plate [2,33,34], between two cylinders [35][36][37][38], between a sphere and a cylinder [39,40], as well as other geometries [41][42][43].…”