The command-line utility scuff-caspol
computes Casimir-Polder potentials for polarizable particles
in the vicinity of material surfaces.
The inputs you supply to scuff-caspol
- a surface-mesh representation of the material surfaces,
- data on the imaginary-frequency polarizability of the
particle(s) you are considering
(scuff-caspol has built-in
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 Casimir-Polder potential.
The outputs you get from scuff-caspol are
- a data file reporting the Casimir-Polder potential for
each atomic species you specified at each evaluation point
scuff-caspol computes the
Casimir-Polder potential at a point x according
to the following formula (working in units with c=1):
Here the integral is over the positive imaginary-frequency
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.
scuff-caspol evaluates the
imaginary-frequency integral by numerical cubature,
with G computed using
scuff-em core-library routines
to solve BEM scattering problems. (More specifically,
to get the full 3×3 matrix at a single point we
solve three separate scattering problems---in which the
incident field is the field of a point electric dipole
source at x oriented in each of the three possible
directions---then compute the scattered field back at
the source point x to obtain the entries of
(The equation above is for the CP potential at zero temperature.
At finite temperatures, the integral becomes a sum over Matsubara
scuff-caspol supports both
zero-temperature and finite-temperature calculations.)
Note that the constant prefactor in the above equation
differs from that found in some other references---for
example, equation (5) of
(arXiv version here).
The different appearance of the formulas may be traced to the
different units used for the polarizability α.
"volume" units, in which α has dimensions of
In contrast, some references measure α in SI units,
in which the numerical value of α differs by a factor
of 4πε0 from its value in volume units.
Indeed, redefining α → 4πε0α
in equation (5) of the above reference and noting that
≣1 in scuff-caspol units
yields the above equation for UCP.
currently supports only compact material surfaces.
(This means that, for example, if you want to study the
Casimir-Polder potential of an atom above an infinite substrate,
you will have to consider a finite-area version of the substrate
and extrapolate to the infinite-area case by considering larger
and larger surface meshes).
Although the core scuff-em library
supports extended surfaces (with Bloch-periodic boundary conditions),
the functionality required to exploit this feature for Casimir-Polder
calculations has not yet been incorporated into
The documentation for scuff-caspol is divided into the