A discrete exterior calculus approach to quantum transport on surfaces

Abstract

We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smooth surface. Was developed a discretization of Schrödinger equation and the associated Green’s functions. Such an approach allowed for the formulation of the tight-binding Hamiltonian based in discrete calculus exterior. We present an efficient algorithm for the calculation of the recursive Green’s functions using numerical tools available for DEC. In addition to working with curved surfaces, our discretization shares the advantages of the Finite Differences Method when submitted to mesh in flat space. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs defined on curved surfaces. We found numerical evidence of a curvature induced integrablechaotic crossover.