Inflow boundary conditions and nonphysical solutions to the Wigner transport equation

Abstract

We investigate the emergence of nonphysical solutions to the steady-state Wigner transport equation on finite-sized simulation domains with inflow boundary conditions. We find that inflow boundary conditions are generally valid, but the wave number uncertainty of injected wave packets has a lower bound that can be significantly higher than usually assumed. Large values of the so-called quantum evolution term (which captures spatial nonlocality in the Wigner transport equation) near simulation-domain boundaries are the cause of spurious reflections, the often-reported discontinuity of the Wigner function at zero wave vector, and negative probabilities. We offer a simple relationship between the lower bound of the wave number uncertainty and simulation parameters that will ensure physical results with inflow boundary conditions.

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

“…For non-trivial interaction mechanisms a closure problem exists in the Wigner formalism [78, p 98]. Other very recent advances of Wigner function methods for electronics (and photonics, but not further discussed here) can be found in a recent special issue [103] and cover, among others, handling of boundary conditions [104][105][106] and modelling and solution approaches [107][108][109][110][111][112][113].…”