Controlled systems

Abstract

This chapter discusses systems subjected to various forms of open-loop or closed-loop control. We begin with a single junction that is characterized only by two tunneling rates describing the probability for jumps in the respective direction. Whereas without feedback one simply obtains Poissonian statistics, modifying the tunneling rate either by open-loop protocols or closed-loop protocols may lead to a modified counting statistics of transferred particles. Here, only closed-loop protocols have the potential to induce significant changes. Second, we consider an electronic pump, where an open-loop protocol may transport electrons against a potential bias. It will be shown that this external control requires energy, without which the pump will not work. The situation is different in feedback control, where the information obtained from a measurement is used to choose the performed control action. The model thus implements an electronic version of Maxwell’s demon: when the information current associated with the measurement is included in the entropy balance, the second law is respected.We also discuss an all-inclusive setup, where the demon is explicitly included in the dynamics. When treated as a whole, the device is nothing but a thermoelectric generator converting a temperature gradient into power. Finally, we outline the potential of feedback control to stabilize quantum coherence by discussing a single qubit that is periodically measured and connected to different reservoirs.