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.