Propagation of Time-Nonlocal Quantum Master Equations for Time-Dependent Electron Transport

TL;DR

This paper develops a time-nonlocal quantum master equation approach for modeling time-dependent electron transport in nano-devices, incorporating arbitrary parameter variations and level broadening effects, with a practical numerical solution scheme demonstrated on a double quantum dot.

Contribution

It introduces a fourth-order quantum master equation with an auxiliary operator method for efficient numerical propagation of time-dependent electron transport.

Findings

The method captures level broadening effects.

The auxiliary operator approach enables practical numerical simulations.

Application to a double quantum dot demonstrates the scheme's viability.

Abstract

Time-resolved electron transport in nano-devices is described by means of a time-nonlocal quantum master equation for the reduced density operator. Our formulation allows for arbitrary time dependences of any device or contact parameter. The quantum master equation and the related expression for the electron current through the device are derived in fourth order of the coupling to the contacts. It is shown that a consistent sum up to infinite orders induces level broadening in the device. To facilitate a numerical propagation of the equations we propose to use auxiliary density operators. An expansion of the Fermi function in terms of a sum of simple poles leads to a set of equations of motion, which can be solved by standard methods. We demonstrate the viability of the proposed propagation scheme and consider electron transport through a double quantum dot.