Variational functionals for the driven quantum harmonic oscillator
Giuseppe Devillanova, Giuseppe Florio, Francesco Maddalena · Complex Variables and Elliptic Equations · 2020
We study some variational problems related to the controllability of the transition between two quantum states of the driven quantum harmonic oscillator. We focus on the existence of minimum points of the total energy functional which is obtained by adding to the cost of the control a term penalizing the distance from the maximum transition probability between given energy states.