Casimir Edge Effects

We compute Casimir forces in open geometries with edges, involving parallel as well as perpendicular semi-infinite plates. We focus on Casimir configurations which are governed by a unique dimensional scaling law with a universal coefficient. With the aid of worldline numerics, we determine this coefficient for various geometries for the case of scalar-field fluctuations with Dirichlet boundary conditions. Our results facilitate an estimate of the systematic error induced by the edges of finite plates, for instance, in a standard parallel-plate experiment. The Casimir edge effects for this case can be reformulated as an increase of the effective area of the configuration.

Figure 1

Sketch of the perpendicular-plates configuration. The minimal distance $a$ between the edge of the upper semi-infinite plate (thick solid line) and the lower infinite plate represents the only dimensionful length scale in the problem.

Figure 2

Contour plot of the Casimir interaction energy-density $\epsilon$ for the perpendicular-plate configuration. The white lines mark the position of the plates to guide the eye. Ensemble parameters: 2000 loops with 10 000 ppl.

Figure 3

Left: sketch of the configuration of a semi-infinite plate parallel to an infinite plate at a distance $a$. A worldline can intersect both plates even if its center of mass is located outside the two plates. Right: sketch of the configuration with two parallel semi-infinite plates at a distance $a$.

Figure 4

Contour plot of the Casimir interaction energy density $\epsilon$ for a semi-infinite plate parallel to an infinite plate. The white lines mark the position of the plates to guide the eye. The energy-density peak extends into the outside region, since worldlines can intersect both plates even if their center of mass is in the outside region. Ensemble parameters: 1000 loops, 10 000 ppl.

Figure 5

Contour plot of the Casimir interaction energy density $\epsilon$ for two parallel semi-infinite plates. The energy-density peak extends into the outside region, since worldlines can intersect both plates even if their center of mass is in the outside region. Ensemble parameters: 2000 loops, 10 000 ppl.