Multiscale Approach for Quantum Systems

Abstract

In this work we propose an iterative multiscale scheme for eigen solutions of the Schrödinger equation with application to the quantum dot array (QDA) systems. The asymptotic expansion predictor and inverse iteration and Rayleigh quotient corrector are introduced. The predictor multiscale formulation is constructed by introducing an asymptotic approach of the original problem and an auxiliary problem. The predictor multiscale solution is corrected by the inverse iteration and the Rayleigh quotient iteration. The numerical results show that the multiscale formulation offers comparable accuracy compared to the solution of the single fine scale model with substantial CPU-time reduction for the tested QDA systems. With the additional corrections by the inverse iteration and Rayleigh quotient, the solution accuracy can be further enhanced.