CPM Seminar

Counter-diabatic driving in many-particle systems

Anatoli Polkovnikov

Boston University

In this talk I will first briefly discuss how we can understand non-adiabatic response in Hamiltonian systems through the perturbation theory in the moving frame. I will show that Coriolis and inertia forces can be understood as leading non-adiabatic corrections to the Born-Oppenheimer approximation and that there are deep connections between the non-adiabatic response and the quantum information geometry. In particular, the inertia mass is closely related to the quantum geometric tensor. Then I will introduce the ideas of counter-diabatic (CD) driving and discuss close connections between the quantum speed limit and the geodesic length defined by the geometric tensor. At the end I will show that the problem of finding CD Hamiltonians can be formulated as a simple minimum action principle, which can be used to develop a variational approach for finding efficient approximate CD driving protocols in complex systems.I will illustrate these ideas with several examples.