Peak, valley and intermediate regimes in the lateral nonretarded Casimir-Polder force

We study the nonretarded Casimir-Polder interaction between a polarizable particle and grounded conducting corrugated surface. For sinusoidal corrugations, one knows that, under the action of the lateral nonretarded Casimir-Polder force, an isotropic particle is always attracted to the nearest corrugation peak, with such behavior called in the present paper as peak regime. Here, considering an anisotropic polarizable particle, and making calculations valid beyond the proximity force approximation (PFA), we show that the lateral force can also attract the particle to the nearest corrugation valley (valley regime), or even to an intermediate point between a peak and a valley (intermediate regime). Moreover, we also show that similar regimes arise in the classical interaction between a neutral polarized particle and a sinusoidal surface. The description of these valley and intermediate regimes, which are out of reach of the predictions based on the PFA, may be relevant for a better understanding of the interaction between anisotropic particles and rough surfaces in classical and quantum physics.