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Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics
: Received: 13 July 2021 / Approved: 14 July 2021 / Online: 14 July 2021 (11:22:11 CEST)
: Received: 12 October 2021 / Approved: 13 October 2021 / Online: 13 October 2021 (11:19:52 CEST)
: 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
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
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