We set up a general density-operator approach to geometric steady-state
pumping through slowly driven open quantum systems. This approach applies to
strongly interacting systems that are weakly coupled to multiple reservoirs at
high temperature, illustrated by an Anderson quantum dot, but shows potential
for generalization. Pumping gives rise to a nonadiabatic geometric phase that
can be described by a framework originally developed for classical dissipative
systems by Landsberg. This geometric phase is accumulated by the transported
observable (charge, spin, energy) and not by the quantum state. It thus differs
radically from the adiabatic Berry-Simon phase, even when generalizing it to
mixed states, following Sarandy and Lidar. Importantly, our geometric
formulation of pumping stays close to a direct physical intuition (i) by tying
gauge transformations to calibration of the meter registering the transported
observable and (ii) by deriving a geometric connection from a driving-frequency
expansion of the current. Our approach provides a systematic and efficient way
to compute the geometric pumping of various observables, including charge,
spin, energy and heat. Our geometric curvature formula reveals a general
experimental scheme for performing geometric transport spectroscopy that
enhances standard nonlinear spectroscopies based on measurements for static
parameters. We indicate measurement strategies for separating the useful
geometric pumping contribution to transport from nongeometric effects. Finally,
we highlight several advantages of our approach in an exhaustive comparison
with the Sinitsyn-Nemenmann full-counting statistics (FCS) approach to
geometric pumping of an observable`s first moment. We explain how in the FCS
approach an "adiabatic" approximation leads to a manifestly nonadiabatic result
involving a finite retardation time of the response to parameter driving.Comment: Major changes: the text was reorganized and improved throughout.
Several typos have been fixed: Note in particular in Eq. (87), (F3) and an
important comment after (107). Throughout Sec V the initial time was
incorrectly set to 0 instead of t_
