Quantum effects in heat and mass transport processes

Abstract

By using the evolution equations for heat and mass fluxes which have been derived from the kinetic equation for the Wigner distribution function of a quantum gas mixture, a quantum effect in mass and heat transport is discussed in this paper. We show that there are transport coefficients associated with mass and heat transport which are proportional to ℏ2 and the curvatures of the external force applied to the system. These quantum effect terms should become observable at low temperatures if the field gradients are comparable to the temperature gradient or the concentration gradients in magnitude. In the case of charge carriers, one of the field gradients can be related to the charge density if the external field is electric, and the quantum effect should be noticeable at low temperatures if the charge density gradient is comparable to the temperature gradient or the concentration gradients of neutral species in magnitude. The said quantum effect means that heat and mass can be driven by second-order gradients (e.g., the curvature) of the external field.