The commandline utility scuffcaspol
computes CasimirPolder potentials for polarizable particles
in the vicinity of material surfaces.
The inputs you supply to scuffcaspol
are
 a surfacemesh representation of the material surfaces,
 data on the imaginaryfrequency polarizability of the
particle(s) you are considering
(scuffcaspol has builtin
polarizability models for several common atomic species,
or you can specify your own models)
 a list of the points in space at which you want to know
the CasimirPolder potential.
The outputs you get from scuffcaspol are
 a data file reporting the CasimirPolder potential for
each atomic species you specified at each evaluation point
you requested.
scuffcaspol computes the
CasimirPolder potential at a point x according
to the following formula (working in units with c=1):
Here the integral is over the positive imaginaryfrequency
axis (ξ is the imaginary frequency); α is
the 3×3 polarizability tensor for the atom or molecule
on which you are computing the CP potential;
and G is the 3×3 matrix representing
the scattering part of the dyadic Green's function at
the point x in the presence of the material bodies
in your geometry.
scuffcaspol evaluates the
imaginaryfrequency integral by numerical cubature,
with G computed using
scuffem corelibrary routines
to solve BEM scattering problems. (More specifically,
to get the full 3×3 matrix at a single point we
solve three separate scattering problemsin which the
incident field is the field of a point electric dipole
source at x oriented in each of the three possible
directionsthen compute the scattered field back at
the source point x to obtain the entries of
G.
(The equation above is for the CP potential at zero temperature.
At finite temperatures, the integral becomes a sum over Matsubara
frequencies.
scuffcaspol supports both
zerotemperature and finitetemperature calculations.)
Note that the constant prefactor in the above equation
differs from that found in some other referencesfor
example, equation (5) of
this paper
(arXiv version here).
The different appearance of the formulas may be traced to the
different units used for the polarizability α.
scuffcaspol uses
"volume" units, in which α has dimensions of
[length^{3}].
In contrast, some references measure α in SI units,
in which the numerical value of α differs by a factor
of 4πε_{0} from its value in volume units.
Indeed, redefining α → 4πε_{0}α
in equation (5) of the above reference and noting that
μ_{0}ε_{0}=1/c^{2}
≣1 in scuffcaspol units
yields the above equation for U^{CP}.
Note:
scuffcaspol
currently supports only compact material surfaces.
(This means that, for example, if you want to study the
CasimirPolder potential of an atom above an infinite substrate,
you will have to consider a finitearea version of the substrate
and extrapolate to the infinitearea case by considering larger
and larger surface meshes).
Although the core scuffem library
supports extended surfaces (with Blochperiodic boundary conditions),
the functionality required to exploit this feature for CasimirPolder
calculations has not yet been incorporated into
scuffcaspol.
The documentation for scuffcaspol is divided into the
following sections.
