Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders

Abstract

We analyze the Casimir force between two parallel infinite metal cylinders, with nearby metal plates (sidewalls), using complementary methods for mutual confirmation. The attractive force between cylinders is shown to have a nonmonotonic dependence on the separation to the plates. This intrinsically multi-body phenomenon, which occurs with either one or two sidewalls (generalizing an earlier result for squares between two sidewalls), does not follow from any simple two-body force description. We can, however, explain the nonmonotonicity by considering the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders, and their images on the nearby plate(s). Furthermore, we show that this effect also implies a nonmonotonic dependence of the cylinder-plate force on the cylinder-cylinder separation.PACS numbers: 12.20. Ds, 42.50.Ct, 42.50.Lc Casimir forces arise from quantum vacuum fluctuations, and have been the subject of considerable theoretical and experimental interest [1,2,3,4]. We consider here the force between metallic cylinders with one or two parallel metal sidewalls ( Fig. 1) using two independent exact computational methods, and find an unusual nonmonotonic dependence of the force on the sidewall separation. These nonmonotonic effects cannot be predicted by commonly used two-body Casimir-force estimates, such as the proximity-force approximation (PFA) [5,6] that is based on the parallel-plate limit, or by addition of Casimir-Polder 'atomic' interactions (CPI) [6,7,8].In previous work, we demonstrated a similar nonmonotonic force between two metal squares in proximity to two parallel metal sidewalls, for either perfect or realistic metals [9]. This work, with perfect-metal cylinders [10], demonstrates that the effect is not limited to squares (i.e., it does not arise from sharp corners or parallel flat surfaces), nor does it require two sidewalls. The nonmonotonicity stems from a competition between forces from transverse electric (TE) and transverse magnetic (TM) field polarizations: In the latter case, the interaction between fluctuating charges on the cylinders is screened by opposing image charges, in the former case it is enhanced by analogous fluctuating image currents. Furthermore, we show that a related nonmonotonic variation arises for the force between the cylinders and a sidewall as a function of separation between the cylinders, a geometry potentially amenable to experiment.Casimir forces are not two-body interactions: quantum fluctuations in one object induce fluctuations throughout the system which in turn act back on the first object. However, both the PFA and CPI view Casimir forces as the result of attractive two-body ("pairwise") interactions. They are reasonable approximations only in certain limits (e.g., low curvature for PFA), and can fail qualitatively as well as quantitatively otherwise. Pairwise estimates fail to account for two important aspects of the Casimir forces in the geometry we consider [11]. First, a monotonic pairwise attrac...

Effect of curvature and confinement on the Casimir-Polder interaction

“…As a consequence, new phenomena can appear, as the nonmonotonicity of the Casimir force for two cylinders [29], and for spheres or atoms in the presence of a perfect metal plate [30]. Similar effects can be expected for the interaction of objects inside cavities due to the confinement of field fluctuations.…”

Many-body effects for critical Casimir forces

“…We use the values provided in Ref. [46] for the coefficients C S1 and C S2 : C S1 = 1.33 eV×(Å) 6 and C S2 = 0.70 eV×(Å) 6 , which correspond to Ne, and C S1 = 17.70 eV×(Å) 6 and C S2 = 10.49 eV×(Å) 6 , which correspond to Ar. As one can infer from Fig.…”

“…These latter effects can lead, e.g., to a strengthening or weakening of the total force acting on a particle surrounded by more than a single other one, a change of sign of that force, or the appearance of stable or unstable configurations. Many-body effects appear in rather diverse systems such as nuclear matter [1], superconductivity [2], colloidal suspensions [3,4], quantumelectrodynamic Casimir forces [5][6][7][8][9][10], polymers [11,12], nematic colloids [13], and noble gases with van der Waals forces acting among them [14][15][16][17]. Each of these systems is characterized by a wide range of time and length scales.…”

Casimir microsphere diclusters and three-body effects in fluids

“…2 turns out to be sufficient to predict the sign of the three-body interaction, although we have no proof that this is a general rule. (In contrast, for non-spherical objects such as cylinders, there can be competing three-body effects that make the sign more difficult to predict, even in vacuum-separated geometries where all pairwise interactions are attractive, which can even lead to a non-monotonic effect [30,31].) Figure 2 also exhibits the interesting phenomenon of bifurcations, in which stable equilibria (solid lines) and unstable equilibria (dashed lines) appear/disappear at some critical h for certain materials and geometries, which is discussed in more detail in Sec.…”

“…29 employed the same formalism in order to study a related geometry consisting of vacuum-separated perfect-metal spheres adjacent to a perfect-metal plate, where it was possible to employ the method of images to reduce the computational complexity dramatically. That work found a three-body phenomenon in which the presence of a metallic plate resulted on a stronger attractive interaction between the spheres, and that this effect becomes more prominent at larger separations [29], related to an earlier three-body effect predicted for cylindrical shapes [30,31]. Here, we examine dielectric spheres and plate immersed in a fluid and therefore cannot exploit the method of images for simplifying the calculation, which makes the calculation much more expensive because of the many oscillatory integrals that must be performed in order to convert between planewaves (scattering off of the plate) and spherical waves (see appendix).…”