Feynman path description of the effects of dephasing of spatial coherences on the transmission and reflection probabilities through a one-dimensional potential

Abstract

In this work, we examine the effects of spatial dephasing of coherences on the transmission and reflection probabilities for electrons with energy E incident to a one-dimensional rectangular barrier of height V 0. Statistical models are presented where the coherence between different scattering pathways or ‘Feynman paths’ undergo dephasing over a length scale, L ϕ . For incident waves with E > V 0, three different dephasing models that attenuate the contributions of spatial coherence to the transmission and reflection probabilities while preserving unitarity (i.e., conserving charge) were investigated. In the tunneling regime (incident waves with E < V 0), however, preserving unitarity requires L ϕ → ∞ , suggesting that elastic tunneling through a rectangular barrier is 100% spatially coherent for these dephasing models. However, wave absorption models are shown to preserve unitarity in the tunneling regime, which is not the case for scattering above the barrier.