Abstract: A quantum impulse is a brief but strong perturbation that produces a sudden change in a wavefunction. I will develop a theory of quantum impulses, distinguishing between ordinary and super impulses: the former paints a phase onto a wavefunction, while the latter deforms the wavefunction under an invertible map. For example, a super impulse might suddenly displace the wavefunction from one location to another, or stretch or squeeze it along a particular direction. Borrowing tools from optimal mass transport theory and shortcuts to adiabaticity, I will show how to design a super impulse that deforms a wavefunction under a desired map. I will illustrate these results using solvable examples. I will also discuss a strong connection between quantum and classical super impulses, expressed in terms of the path integral formulation of quantum mechanics. The results I will present are derived for evolution under the time-dependent Schrödinger equation, but they apply as well to the time-dependent Gross-Pitaevskii equation, and therefore may be applicable to Bose-Einstein condensates.
*The lunch could not be cancelled, so it will be served at noon. You will need to print your first an last name on the sign-up sheet.*