Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics

Version 1 : Received: 13 July 2021 / Approved: 14 July 2021 / Online: 14 July 2021 (11:22:11 CEST)
Version 2 : Received: 12 October 2021 / Approved: 13 October 2021 / Online: 13 October 2021 (11:19:52 CEST)
Version 3 : Received: 15 January 2022 / Approved: 17 January 2022 / Online: 17 January 2022 (09:04:34 CET)

A peer-reviewed article of this Preprint also exists.

Journal reference: International Journal of Theoretical Physics volume 2022
DOI: 10.1007/s10773-022-05124-8


We derive the thermal noise spectrum of the Fourier transform of the electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers. It is important to stress that no additional assumptions at all were used in this straightforward proof.


fluctuations; noise spectra; longitudinal and transverse electric fields; Nyquist noise; photon number noise


PHYSICAL SCIENCES, Condensed Matter Physics

Comments (1)

Comment 1
Received: 13 October 2021
Commenter: Ladislaus Banyai
Commenter's Conflict of Interests: Author
Comment: The paper was einriched with new references and comments. One of them is the connection to the known results of classical plasma theory. We introduced several new comments. We also restructured the paper putting two Sections into the Appendices in order to help following the main line. Some  small print errors were eliminated.
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 1
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.