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)
Bányai, L.A.; Bundaru, M.; Gartner, P. Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics. International Journal of Theoretical Physics 2022, 61, doi:10.1007/s10773-022-05124-8.
Bányai, L.A.; Bundaru, M.; Gartner, P. Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics. International Journal of Theoretical Physics 2022, 61, doi:10.1007/s10773-022-05124-8.
Bányai, L.A.; Bundaru, M.; Gartner, P. Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics. International Journal of Theoretical Physics 2022, 61, doi:10.1007/s10773-022-05124-8.
Bányai, L.A.; Bundaru, M.; Gartner, P. Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics. International Journal of Theoretical Physics 2022, 61, doi:10.1007/s10773-022-05124-8.
Abstract
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.
Keywords
fluctuations; noise spectra; longitudinal and transverse electric fields; Nyquist noise; photon number noise
Subject
Physical Sciences, Condensed Matter Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Commenter: Ladislaus Banyai
Commenter's Conflict of Interests: Author