Pumping in quantum dots and non-Abelian matrix Berry phases

TL;DR

This paper explores how non-Abelian Berry phases influence charge pumping in quantum dots, showing that the pumped charge correlates with the matrix Berry phase and varies with each adiabatic cycle.

Contribution

It provides an exact solution to the time-dependent Schrödinger equation for adiabatic processes, linking matrix Berry phases to charge pumping in quantum dots.

Findings

Pumped charge is related to finite matrix Berry phases.

Charge per cycle varies with consecutive adiabatic cycles.

Exact solutions demonstrate the role of non-Abelian phases in quantum dot pumping.

Abstract

We have investigated pumping in quantum dots from the perspective of non-Abelian (matrix) Berry phases by solving the time dependent Schr{\"o}dinger equation exactly for adiabatic changes. Our results demonstrate that a pumped charge is related to the presence of a finite matrix Berry phase. When consecutive adiabatic cycles are performed the pumped charge of each cycle is different from the previous ones.