Uncertainty Quantification for Charge Transport in GNRs Through Particle Galerkin Methods for the Semiclassical Boltzmann Equation (Communications in Computational Physics, 2025)
In this article, we investigate some issues related to the quantification ofuncertainties associated with the electrical properties of graphene nanoribbons. Theapproach is suited to understand the effects of missing information linked to the difficulty of fixing some material parameters, such as the band gap, and the strength ofthe applied electric field. In particular, we focus on the extension of particle Galerkinmethods for kinetic equations in the case of the semiclassical Boltzmann equation forcharge transport in graphene nanoribbons with uncertainties. To this end, we developan efficient particle scheme which allows us to parallelize the computation and then,after a suitable generalization of the scheme to the case of random inputs, we presenta Galerkin reformulation of the particle dynamics, obtained by means of a generalizedPolynomial Chaos approach, which allows the reconstruction of the kinetic distribution. As a consequence, the proposed particle-based scheme preserves the physicalproperties and the positivity of the distribution function also in the presence of a complex scattering in the transport equation of electrons. The impact of the uncertainty ofthe band gap and applied field on the electrical current is analysed.