Adiabatic Quantum Transport: Quantization and Fluctuations

TL;DR

This paper applies Quillen's local index theorem to analyze charge transport in quantum systems, revealing how adiabatic curvature splits into integral and fluctuating parts related to quantum chaos.

Contribution

It introduces a novel application of Quillen's local index theorem to decompose adiabatic curvature into explicit and fluctuating components in quantum transport.

Findings

Adiabatic curvature can be split into integral and fluctuating parts.

Fluctuating part has a natural interpretation in quantum chaos.

Provides a new mathematical framework for quantum charge transport analysis.

Abstract

Quillen's local index theorem is used to study the charge transport coefficients (adiabatic curvature) associated to the ground state of a Schr\"odinger operator for a charged (spinless) particle on a closed, multiply connected surface. The formula splits the adiabatic curvature into an explicit integral part and a fluctuating part which has a natural interpretation in terms of quantum chaos.