## Proximity force approximation and specular reflection: Application of the WKB limit of Mie scattering to the Casimir effect

- The electromagnetic Casimir interaction between two spheres is studied within the scattering approach using the plane-wave basis. It is demonstrated that the proximity force approximation (PFA) corresponds to the specular-reflection limit of Mie scattering. Using the leading-order semiclassical WKB approximation for the direct reflection term in the Debye expansion for the scattering amplitudes, we prove that PFA provides the correct leading-order term in the small-distance limit for arbitrary materials and temperatures in the sphere-sphere and the plane-sphere geometry. Our derivation implies that only a small section around the points of closest approach between the interacting spherical surfaces contributes in the PFA regime. The corresponding characteristic length scale is estimated from the width of the Gaussian integrand obtained within the saddle-point approximation. At low temperatures, the area relevant for the thermal corrections is much larger than the area contributing toThe electromagnetic Casimir interaction between two spheres is studied within the scattering approach using the plane-wave basis. It is demonstrated that the proximity force approximation (PFA) corresponds to the specular-reflection limit of Mie scattering. Using the leading-order semiclassical WKB approximation for the direct reflection term in the Debye expansion for the scattering amplitudes, we prove that PFA provides the correct leading-order term in the small-distance limit for arbitrary materials and temperatures in the sphere-sphere and the plane-sphere geometry. Our derivation implies that only a small section around the points of closest approach between the interacting spherical surfaces contributes in the PFA regime. The corresponding characteristic length scale is estimated from the width of the Gaussian integrand obtained within the saddle-point approximation. At low temperatures, the area relevant for the thermal corrections is much larger than the area contributing to the zero-temperature result.…

Author: | Benjamin SprengORCiD, Michael HartmannORCiD, Vinicius Henning, Paulo A. Maia NetoORCiD, Gert-Ludwig IngoldORCiDGND |
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URN: | urn:nbn:de:bvb:384-opus4-399547 |

Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/39954 |

Parent Title (English): | Physical Review A |

Type: | Article |

Language: | English |

Year of first Publication: | 2018 |

Publishing Institution: | Universität Augsburg |

Release Date: | 2018/08/29 |

Volume: | 97 |

Issue: | 6 |

First Page: | 062504 |

DOI: | https://doi.org/10.1103/PhysRevA.97.062504 |

Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |

Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik | |

Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I | |

Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |

Licence (German): | Deutsches Urheberrecht |