Diffusive solver: a diffusion-equations solver based on FEniCS

TL;DR

The paper introduces a Python package based on FEniCS for solving coupled diffusion equations in condensed matter physics, enabling automatic computation of conductivities and responsivities for systems with multiple degrees of freedom.

Contribution

It presents a novel, flexible diffusion-equation solver that handles multiple degrees of freedom and automatically computes linear response properties, tailored for condensed matter transport problems.

Findings

Successfully solves magneto-transport and thermoelectric transport examples

Automates calculation of conductivities and responsivities

Demonstrates applicability to systems with multiple degrees of freedom

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.