# Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties

## Abstract

We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett. 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface-surface separation at which finite-size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.

- Authors:

- Department Of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
- (United States)
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 22038563

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 77 NANOSCIENCE AND NANOTECHNOLOGY; CASIMIR EFFECT; COMPUTERIZED SIMULATION; DIELECTRIC MATERIALS; ELECTRIC CURRENTS; MAGNETIC MATERIALS; MAGNETIC SURFACES; QUANTUM ELECTRODYNAMICS; SURFACES; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Reid, M. T. Homer, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, White, Jacob, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, Johnson, Steven G., and Department Of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
```*Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.010503.

```
Reid, M. T. Homer, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, White, Jacob, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, Johnson, Steven G., & Department Of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
```*Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties*. United States. doi:10.1103/PHYSREVA.84.010503.

```
Reid, M. T. Homer, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, White, Jacob, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, Johnson, Steven G., and Department Of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Fri .
"Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties". United States. doi:10.1103/PHYSREVA.84.010503.
```

```
@article{osti_22038563,
```

title = {Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties},

author = {Reid, M. T. Homer and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and White, Jacob and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and Johnson, Steven G. and Department Of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139},

abstractNote = {We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett. 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface-surface separation at which finite-size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.},

doi = {10.1103/PHYSREVA.84.010503},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}