Investigation of quantum transport by means of O(N) real-space methods

TL;DR

This paper introduces an efficient O(N) real-space method based on orthogonal polynomials to study quantum transport, providing new insights into phenomena like quantum Hall effects and potential applications in large-scale computations.

Contribution

Develops a novel O(N) real-space approach using orthogonal polynomials for quantum transport analysis, enabling studies of complex systems and large-scale computational problems.

Findings

Analysis of quantum Hall systems reveals new universalities.

Method offers insights into metal-insulator transitions.

Potential applications include RKKY interactions and large-scale simulations.

Abstract

Quantum transport for different systems is investigated by developing the Kubo formula on a basis of orthogonal polynomials. Results on quantum Hall systems are presented with particular attention to metal insulator transitions and new universalities. Other potential applications of the present method for RKKY mesoscopic interaction and insight for large scale computational problems, are given.