Efficient Adaptive Computation of the Dynamics of Mott Transistors

TL;DR

This paper develops and analyzes adaptive Magnus-type integrators for simulating Mott transistor dynamics, effectively handling rapidly changing electromagnetic fields with error estimators for improved accuracy.

Contribution

It introduces an adaptive numerical method tailored for Mott transistor simulations, addressing challenges posed by unsmooth external potentials.

Findings

Adaptive integrators improve accuracy in Mott transistor simulations.

Error estimators effectively guide time step selection.

Adaptive approach outperforms fixed-step methods in complex scenarios.

Abstract

We investigate time-adaptive Magnus-type integrators for the numerical approximation of a Mott transistor. The rapidly attenuating electromagnetic field calls for adaptive choice of the time steps. As a basis for step selection, asymptotically correct defect-based estimators of the local error are employed. We analyze the error of the numerical approximation in the presence of the unsmooth external potential and demonstrate the advantages of the adaptive approach.