Abstract
By analogy with the fundamental quantum units of electrical conductance G₀^e=2 e²/h and thermal conductance K₀^t=2 K_B² T/h we define a fundamental quantum unit of conductance, G₀^m, and diffusion of a massive gas of atomic particles, respectively given by G₀^m=m²/h , D₀=h/m with h the Planck constant, K_B the Boltzmann constant, T the absolute temperature, e the unit charge and m the mass of the atomic gas particle that move balistically in a one dimensional medium of length L. The effect of scattering can be accounted for by introducing an appropriate transmission probability in analogy with the quantum electrical conductance model introduced by Landauer in 1957. For an electron gas G₀^m=1.25 × 10⁻²⁷ Kg²/(J s) and D₀ = 7.3 × 10⁻³ m²/s, and we found a quantum expression for the generalized Einstein relation that writes G₀^e = 2e²m/h² D₀