Thermal and quantum fluctuations are ubiquitous in nature. Starting with the successful prediction of Planck's blackbody radiation spectrum, they have played an important role in quantum electrodynamics ever since. Perhaps somehow unexpectedly, they are also responsible for the appearance of forces between neutral objects such as the Casimir-Polder force [1]. While these interactions fall off rapidly with distance, they turn out to be relevant in a large variety of physical systems of vastly different length scales.
Since analytical investigations are only possible for a few highly symmetric cases, we have recently introduced a numerical scheme to calculate the Casimir-Polder interaction using the finite-element-based discontinuous Galerkin time-domain (DGTD) method [2]. This allows for the investigation of these forces in a broad range of different setups, including nonlocal materials and finite temperatures. We illustrate the flexibility and the validity of our approach with a few examples.
[1] F. Intravaia, C. Henkel, and M. Antezza, Fluctuation-Induced Forces Between Atoms and Surfaces: The Casimir-Polder Interaction, in Casimir Physics, edited by D. Dalvit, P. Milonni, D. Roberts, and F. da Rosa, Vol. 834 (Springer, 2011)
[2] K. Busch, M. König, and J. Niegemann, Discontinuous Galerkin Methods in Nanophotonics, Laser & Photonics Reviews 5, 6 (2011)