Diffusive solver: a diffusion-equations solver based on FEniCS

Abstract

Many steady-state transport problems in condensed matter physics can be reduced to a set of coupled diffusion equations. This is true in particular when relaxation processes are sufficiently fast that the system is in the diffusive --opposite of ballistic-- regime. Here we describe a python package, based on FEniCS, that solves this type of problems with an arbitrary number degrees of freedom that can represent charge, spin, energy, band or valley flavours. Generalized conductivities and responsivities, characterizing completely the linear response of the system to external biases and sources, are automatically computed from the solutions. We solve two simple example of magneto-transport and thermoelectric transport for illustrative purpose.