Does the Finite Size of Electrons Affect Quantum Noise in Electronic Devices?

Quantum transport is commonly studied with the use of quasi-particle infinite-extended states. This leads to a powerful formalism, the scattering-states theory, able to capture in compact formulas quantities of interest, such as average current, noise, etc.. However, when investigating the spatial size-dependence of quasi-particle wave packets in quantum noise with exchange and tunneling, unexpected new terms appear in the quantum noise expression. For this purpose, the two particle transmission and reflection probabilities for two initial one-particle wave packets (with opposite central momentums) spatially localized at each side of a potential barrier are studied. After the interaction, each wave packet splits into a transmitted and a reflected component. It can be shown that the probability of detecting two (identically injected) electrons at the same side of the barrier is different from zero in very common (single or double barrier) scenarios. This originates an increase of quantum noise which cannot be obtained through the scattering states formalism.