Adiabaticity in quantum transport

It is commonly assumed that electrons evolve adiabatically in quantum transport devices, and so remain in the same transverse quantum state throughout the system. This model simplifies the analysis of such devices and the model correctly predicts that the conductance of a system containing a number of constrictions is quantised with a value equal to the conductance of the narrowest constriction. In this paper the validity of the adiabatic model for the evolution of the electronic wavefunctions is investigated via an analysis of the behaviour of a wavefunction in a one-dimensional potential well whose width increases with time. It is found that the evolution becomes strongly non-adiabatic no matter how small the rate of increase in the width of the well. This invalidates the previous interpretation of the origin of a quantised conductance in devices containing several constrictions. However, it is shown that the quantisation of the conductance in these devices can be explained by replacing the requirement of adiabaticity in the evolution of the transverse electronic wavefunctions with the requirement of reversibility.