**Kazunari Hashimoto 1,\*,† and Chikako Uchiyama 1,2,\*,†**


Received: 8 July 2019; Accepted: 23 August 2019; Published: 28 August 2019

**Abstract:** The ability to control quanta shown by quantum pumping has been intensively studied, aiming to further develop nano fabrication. In accordance with the fast progress of the experimental techniques, the focus on quantum pumping extends to include the quicker transport. For this purpose, it is necessary to remove the "adiabatic" or "slow" condition, which has been the central concept of quantum pumping since its first proposal for a closed system. In this article, we review the studies which go beyond the conventional adiabatic approximation for open quantum systems to transfer energy quanta and electron spins with using the full counting statistics. We also discuss the recent developments of the nonadiabatic treatments of quantum pumping.

**Keywords:** nonadiabaticity; quantum heat pumping; spin pumping; relaxation
