Geothermal Casimir phenomena for the sphere-plate and cylinder-plate configurations

We investigate the nontrivial interplay between geometry and temperature in the Casimir effect for the sphere-plate and cylinder-plate configurations. At low temperature, the thermal contribution to the Casimir force is dominated by this interplay, implying that standard approximation techniques such as the proximity force approximation (PFA) are inapplicable even in the limit of small surface separation. Thermal fluctuations on scales of the thermal wavelength lead to a delocalization of the thermal force density at low temperatures. As a consequence, the temperature dependence strongly differs from naive expectations. Most prominently, thermal forces can develop nonmonotonic behavior below a critical temperature. We perform a comprehensive study of such geothermal phenomena in these Casimir geometries, using analytical and numerical worldline techniques for Dirichlet scalar fluctuations.