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16 - Stochastic Fields and Sources

Published online by Cambridge University Press:  31 October 2025

Lukas Novotny
Affiliation:
Eidgenössische Technische Hochschule Zürich
Bert Hecht
Affiliation:
Julius-Maximilians-Universität Würzburg, Germany
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Summary

Thermal and zero-point fluctuations of charges and electromagnetic fields give rise to fluctuation-induced forces, known as dispersion forces. To understand these forces, we first discuss the properties of stationary stochastic fields and derive fluctuation–dissipation theorems for both fields and sources. Fluctuating sources give rise to Johnson noise in resistors and to blackbody radiation and heat transfer. For a pair of polarizable particles, we derive the Casimir–Polder potential and evaluate it for short and large separations, which renders the Van der Waals and the Casimir force, respectively. For a particle moving in a thermal field, we find a viscous force, referred to as vacuum friction. We show that zero-point fluctuations are responsible for shot noise in optical power measurements and for radiation pressure shot noise exerted on irradiated objects. Shot noise is responsible for measurement imprecision and radiation pressure shot noise for measurement backaction, the disturbance of an object by the measuring optical field. We show that imprecision and backaction noise set a limit to measurement accuracies, known as the standard quantum limit, and that their product is fundamentally bound by the so-called Heisenberg limit.

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Publisher: Cambridge University Press
Print publication year: 2025

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  • Stochastic Fields and Sources
  • Lukas Novotny, Eidgenössische Technische Hochschule Zürich, Bert Hecht, Julius-Maximilians-Universität Würzburg, Germany
  • Book: Principles of Nano-Optics
  • Online publication: 31 October 2025
  • Chapter DOI: https://doi.org/10.1017/9781108781503.019
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  • Stochastic Fields and Sources
  • Lukas Novotny, Eidgenössische Technische Hochschule Zürich, Bert Hecht, Julius-Maximilians-Universität Würzburg, Germany
  • Book: Principles of Nano-Optics
  • Online publication: 31 October 2025
  • Chapter DOI: https://doi.org/10.1017/9781108781503.019
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Stochastic Fields and Sources
  • Lukas Novotny, Eidgenössische Technische Hochschule Zürich, Bert Hecht, Julius-Maximilians-Universität Würzburg, Germany
  • Book: Principles of Nano-Optics
  • Online publication: 31 October 2025
  • Chapter DOI: https://doi.org/10.1017/9781108781503.019
Available formats
×