Romanticism and beyond (1834-1849)

Numerical methods for fluctuation-driven interactions between dielectrics

“…This is what one would expect since PFA misses to consider collective effects, which are more important when larger positions of the surfaces are close. These violations of the proximity-force-approximation are not peculiar to the classical regime and similar effects are also found for the quantum system for significantly non-flat geometries [11,12].…”

“…For more complex geometries this problem has been approached from various directions, both in its full quantum formulation, and in the high temperature, classical, regime. The range of techniques used is very wide, including Green's function formulations [11], world-line numerics [12], and path-integral formulations [13]. These techniques have allowed for great progress in linking the theory with experimental observation, but, as of now, no general method is avaliable for arbitrary geometries and arbitrary values of the parameters.…”

Fluctuation-induced interactions between dielectrics in general geometries

“…Given the limitations of all analytic methods, which are in practice only capable of studying very regular geometries, numerical approaches have been developed. These methods have been limited both by storage space required and by long computational times, making it possible to study only two-dimensional systems, or three-dimensional systems translationally invariant in one direction [9,10]. It is only very recently that more powerful methods have been developed based on the numerical calculation of the Maxwell stress tensor [11].…”