Quantum pumping and dissipation: from closed to open systems

TL;DR

This paper analyzes quantum pumping in closed and open systems, deriving formulas for conductance contributions, discussing dissipation, and connecting to established theories like Landauer and Onsager reciprocity.

Contribution

It introduces Green function and S matrix formulas for conductance terms, clarifies the infinite system limit, and generalizes fluctuation-dissipation relations in quantum pumping.

Findings

Derived Green function and S matrix formulas for conductance components.

Clarified the infinite system limit and its implications.

Connected quantum pumping theory with Landauer and Onsager principles.

Abstract

Current can be pumped through a closed system by changing parameters (or fields) in time. The Kubo formula allows to distinguish between dissipative and non-dissipative contributions to the current. We obtain a Green function expression and an $S$ matrix formula for the associated terms in the generalized conductance matrix: the "geometric magnetism" term that corresponds to adiabatic transport; and the "Fermi golden rule" term which is responsible to the irreversible absorption of energy. We explain the subtle limit of an infinite system, and demonstrate the consistency with the formulas by Landauer and Buttiker, Pretre and Thomas. We also discuss the generalization of the fluctuation-dissipation relation, and the implications of the Onsager reciprocity.