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Computing Casimir-Polder Potentials with scuff-caspol

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 are

  • 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 you requested.

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 G.

(The equation above is for the CP potential at zero temperature. At finite temperatures, the integral becomes a sum over Matsubara frequencies. 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 this paper (arXiv version here). The different appearance of the formulas may be traced to the different units used for the polarizability α. scuff-caspol uses "volume" units, in which α has dimensions of [length3]. 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 μ0ε0=1/c2 ≣1 in scuff-caspol units yields the above equation for UCP.

Note: scuff-caspol 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 scuff-caspol.

The documentation for scuff-caspol is divided into the following sections.

Table Of Contents
1. scuff-caspol Tutorial and Examples
2. scuff-caspol Command-Line Reference
3. scuff-caspol Output File Reference

Core Library

Computing Casimir-Polder Potentials with scuff-caspol, by Homer Reid
Last Modified: 11/16/16