The fundamental units of generalized quantum conductance and quantum diffusion

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 classicaó 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.We provide quantum-relativistic expressions for the generalized Einstein relations between generalized conductance and diffusion of the considered quasi-particles. The fundamental quantum units of dimensionless, electric, neutral mass, photon/phonon energy, and the longitudinal diffusion coefficient are provided. Quantum relativistic expressions are given for the generalized Einstein relations between generalized conductance and diffusion of the considered quasiparticles. It is shown that the fundamental role played by physical action is essential under both classical and quantum relativistic conditions. Finally, the unifying role of quasi-particle physics in connecting classical and quantum relativistic conductance is confirmed.