Anomalous Temperature Dependence of the Casimir Force for Thin Metal Films

Within the framework of the Drude dispersive model, we predict an unusual nonmonotonic temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk metal sphere (lens). The experimental observation of the predicted decreasing temperature dependence of the Casimir force can put an end to the long-standing discussion on the role of the electron relaxation in the Casimir effect.

Figure 1

(a),(b) Geometry of the problem. The Casimir attraction of a thin metal film (in red) to an ideal plane bulk metal [in (a)] and to an ideal metal sphere [in (b)]. (c)–(f) The temperature dependence of the Casimir force of attraction of strontium (upper red curve in (c) and (d), Barium [middle black curve in (c) and (d)], cesium (bottom green curve in (c) and d), and virtual (nonexistent) metal (dashed blue curve in (e) and (f) films to an ideal plane bulk metal (for (c) and (e) and to a metal sphere of radius $R=5\mathrm{cm}$ (for (d) and (f). The separation $a$ is ${10}^{-5}\mathrm{cm}$ for all curves. Other parameters are pointed in the text. Even though the theoretical predictions can show a nonmonotonic (e),(f) behavior of $F(T)$, only the decreasing (with temperature) part of the force could be observed for the chosen materials. Note that $|f|$ in panels (c),(e) refer to the modulus of the Casimir force per unit area, while $|F|$ in panels (d),(f) correspond to the modulus of the total Casimir force.