SpaRTaNS: Spatially Resolved Transport of Non-equilibrium Species

At steady state, non-equilibrium transport of carriers, such as electrons and phonons, is given by the semi-classical Boltzmann transport equation (BTE). In general, the BTE is a six-dimensional non-linear integro-differential equation which is non-trivial to solve. Typically, one proceeds by linearizing the BTE and approximating the collision operator using simple functional forms which relax towards a local equilibrium. Recently, there have been considerable efforts in retaining the full state-resolution of the collision operator, applied in computing bulk transport properties, effectively neglecting spatial variations in the resulting carrier distribution function.

Here, we present SpaRTaNS (Spatially Resolved Transport of Non-equilibrium Species): a recursive solver to the BTE which retains both state- and space-resolution. We demonstrate SpaRTaNS' utility by solving a recently-proposed non-equilibrium transport problem with distinct spatial signatures, namely electron "hydrodynamics". Specifically, we investigate the role of microscopic interactions in electron hydrodynamics by using crystal symmetries and conservation laws to randomly generate physically-allowed scattering matrices and quantify their variability on macroscopic observables such as current density curvature.