Iterative path integral summation for nonequilibrium quantum transport

TL;DR

This paper introduces a numerically exact iterative path integral method for calculating real-time quantum transport in nonequilibrium systems, effectively incorporating non-Markovian effects and finite memory times.

Contribution

The authors develop a deterministic iterative summation approach (ISPI) that accurately computes nonequilibrium quantum transport properties, including lead self-energies and non-Markovian effects.

Findings

Accurate computation of charge current in quantum transport.

Effective inclusion of non-Markovian lead effects.

Numerical validation of the method's precision.

Abstract

We have developed a numerically exact approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the generating function of nonequilibrium observables of interest, e.g., the charge current or dynamical quantities of the central part. Self-energies due to the leads, being nonlocal in time, are fully taken into account within a finite memory time, thereby including non-Markovian effects. Numerical results are extra-polated first to vanishing (Trotter) time discretization and, second, to infinite memory time...