Multi-scale Non-equilibrium Molecular Dynamics Formulation For Casimir Energy

Formulation of the Casimir effect using multi-scale nonequilibrium molecular dynamics (MS-NEMD) is addressed in this paper. Except in the case of parallel plates, simulation of the Casimir effect is a challenging task. MS-NEMD may offer a suitable approach in estimating the Casimir effect for complicated geometries and irregular objects. MS-NEMD consists of a fine scale molecular dynamics simulation coupled with a coarse scale finite element approach. In this paper, the molecular dynamics approach deals with every molecule when subjected to the Casimir effect from a point on an opposing object. Therefore, every point of an irregular object is treated according to the Casimir parallel plate formalism when the dimension of the plate is limited to a single point. Finite element (FE) approach deals with geometrical complication of the object being analyzed. In MS-NEMD, FE nodes act as thermostats, and the atoms associated with each node are considered at local equilibrium within one coarse scale. Atoms are subjected to external force due to Casimir pressure which is summed with the effect of thermostats at each atom. This approach is not proven to provide the exact solution. However, the formulation of the Casimir effect using MS-NEMD may be suitable in estimating the effect for complicated geometries.