Fundamental quantum and relativistic formulation of thermal noise and linear conductance in an 1D quasi-particle ensemble under ballistic transport-regime

TL;DR

The paper develops a quantum-relativistic framework for thermal noise and linear conductance in a 1D quasi-particle ensemble under ballistic transport, addressing the vacuum catastrophe via the Casimir effect. It extends Nyquist-type noise to quantum regimes and derives universal 1D conductance units for various quasi-particles, including a photon-case expression tied to Planck statistics. A novel link is proposed between black-body photon-number fluctuations and atomic spectral constants, suggesting the inverse of the fine-structure constant emerges from photon-number variance. The combined approach connects mesoscopic transport, quantum fluctuations, and atomic spectroscopy, with potential experimental crossovers in photon counting and spectral interpretation.

Abstract

We investigate quantum and quantum-relativistic effects associated with the noise power spectrum and the fluctuation--dissipation relation between current--noise spectra and linear--response conductance at low frequencies of the electromagnetic field. At high frequencies, vacuum catastrophe is shown to be avoided by the presence of Casimir force. At low frequencies, the quantum effect associated with one--dimensional structures under the conditions of ballistic transport typical at the nanometric scale length are briefly reviewed in terms of a universal quasi-particle approach. The case of a photon gas inside an appropriate black-body cavity is found to provide a physical interpretation of the lines spectra of atomic elements within an exact statistical approach based on a physical interpretation of the fine structure constant, $α=1/137.0560$.

Figures (1)

• Figure 1: Plot summarizing the variance of the photon numbers $\overline {\delta N^2}$ (or the inverse fine--structure constant of the H atom $1/\alpha$) as a function of the photon energy $k_BT$ and average photon number $\overline N$ including the available emission spectra of the Paschen, Balmer and Lyman series (colored shades areas), obtained by the statistical scheme property of the black--body photon gas as described by Planck's distribution law. The universal behavior of the Fano factor is evidenced by the straight line representing the law: $\overline{\delta N^2} = \gamma \overline{N}$. Analogous spectra of other atoms pertaining to the Mendeleev periodic table could be shown in the same way. The two large points correspond to the values of the hydrogen fine-structure constant (FSC) and hyperfine--structure constant (HFSC). The reverse procedure should require the determination of the average number of photons under the conditions of temperature and volume $L_{\frac{1}{\alpha}} T_{\frac{1}{\alpha}} = 1.7 \times 10^{-2} \ (\mathrm{m\ K})$ of the black-body at thermal equilibrium.