Infrared finite scattering theory in quantum field theory and quantum gravity

Prabhu, Kartik; Satishchandran, Gautam; Wald, Robert M.

doi:10.1103/PhysRevD.106.066005

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.

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