The fundamental units of generalized quantum conductance and quantum diffusion

TL;DR

This paper develops a unified theory of quantum conductance and diffusion for various quasi-particle currents, bridging classical, quantum, and relativistic regimes with a focus on a generalized conductance unit.

Contribution

It introduces a novel generalized conductance framework for quasi-particles, connecting classical models to quantum and relativistic regimes, and defines a fundamental quantum conductance unit.

Findings

Derived the fundamental quantum unit of conductance for multiple currents.

Extended the diffusion coefficient from classical to quantum and relativistic regimes.

Established a connection between Planck's constant and a classical action considering statistics.

Abstract

Although quantum transport at the nanoscale has received widespread attention since Landauer's pioneering work in 1957, we remark, that a general theory that sheds light on the difference between classical and quantum relativistic physical models is still lacking. By considering a classical 3D gas of non-interacting quasi.particles, the article presents a unified theory that provides a generalized conductance of dimensionless quasi-particles, neutral massive, electric, thermal, and photon currents. The investigation begins with an analogy between the original Drude model of 1900 and a modified Drude model of quasi-particles, which includes a ballistic transport regime and is independent of statistics (excluding Bose-Einstein condensation). Next, we construct connections between the quasi-particle unit in the modified Drude model and the carrier unit in dimensionless, electric, massive neutral, phonon, and photon currents. By establishing a connection between Planck's constant $h$ and a classica\`o action that takes into account the correct statistics, $h_s$, we derive the fundamental quantum unit of conductance for any of the mentioned currents. We further extend the diffusion coefficient of quasi-particles from the classical regime to the quantum and relativistic regimes.