# Geometrical optimization of pumping power under adiabatic parameter driving

## TL;DR

This paper investigates how to optimize the power output of adiabatic pumping in mesoscopic devices by balancing the contour length and driving speed, demonstrating an optimal cycle for maximum power.

## Contribution

It introduces a method to optimize pumping power by balancing cycle duration and contour length under adiabatic constraints, confirmed through quantum dot simulations.

## Key findings

- Existence of an optimal cycle period for maximum power
- Trade-off between contour length and pumping power
- Validation through quantum dot charge pumping simulations

## Abstract

Adiabatic pumping is a fundamental concept in the time-dependent transport of mesoscopic devices. To maximize pumping performance, i.e., the amount of pumping per unit time, it is necessary to carefully manage the driving speed, which should be sufficiently less than the {\it limited speed}, an upper bound of the driving speed below which non-adiabatic effects are negligible. In general, the amount of pumping increases as the contour of the driving parameter lengthens, however a long contour diminishes the pumping power because it requires more time per cycle under the limited speed constraint. We consider this trade-off carefully and show that there should exist an optimized period and contour to maximize the power of adiabatic pumping. We confirm this conclusion based on the results of charge pumping using a single-level quantum dot.