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A quantum impulse is a brief but strong perturbation that produces a sudden change in a wave function ψ (x). We develop a theory of quantum impulses, distinguishing between ordinary and super impulses. An ordinary impulse paints a phase onto ψ, while a super impulse—the main focus of this paper—deforms the wave function under an invertible map, μ : x → x′. Borrowing tools from optimal-mass-transport theory and shortcuts to adiabaticity, we show how to design a super impulse that deforms a wave func- tion under a desired map μ and we illustrate our results using solvable examples. We point out a strong connection between quantum and classical super impulses, expressed in terms of the path-integral formu- lation of quantum mechanics. We briefly discuss hybrid impulses, in which ordinary and super impulses are applied simultaneously. While our central results are derived for evolution under the time-dependent Schrödinger equation, they apply equally well to the time-dependent Gross-Pitaevskii equation and thus may be relevant for the manipulation of Bose-Einstein condensates. 

Abstract Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes—which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.