# Lindblad approach to spatio-temporal quantum dynamics of phonon-induced carrier capture processes

## TL;DR

This paper introduces a Lindblad superoperator model to describe phonon-induced carrier capture in nanostructures, providing a quantum dynamics framework that captures ultrafast processes with comparisons to non-Markovian methods.

## Contribution

The work develops a Lindblad-based nonlinear density matrix approach tailored for spatio-temporal quantum dynamics of carrier capture, offering an alternative to existing non-Markovian models.

## Key findings

- Lindblad approach effectively models ultrafast carrier capture processes.
- Comparison shows advantages and limitations of Lindblad versus non-Markovian methods.
- Model captures quantum effects at nanoscales with computational efficiency.

## Abstract

In view of the ultrashort spatial and temporal scales involved, carrier capture processes in nanostructures are genuine quantum phenomena. To describe such processes, methods with different levels of approximations have been developed. By properly tailoring the Lindblad-based nonlinear single-particle density matrix equation provided by an alternative Markov approach, in this work we present a Lindblad superoperator to describe how the phonon-induced carrier capture affects the spatio-temporal quantum dynamics of a flying wave packet impinging on a quantum dot. We compare the results with non-Markovian quantum kinetics calculations and discuss the advantages and drawbacks of the two approaches.