On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control

Abstract

We study the stability of the Schrödinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schrödinger equation by the difference of their Hamiltonians. The stability theorem obtained in this article provides a sharper bound than those previously obtained in the literature. This makes it a potentially useful tool for time-dependent problems in Quantum Physics, in particular for Quantum Control. We apply this result to prove two theorems about global approximate controllability of infinite-dimensional quantum systems. These results improve and generalise existing results on infinite-dimensional quantum control.

arXiv admin note: text overlap with arXiv:2108.00495

References in corpus (4)

• One bound to rule them all: from Adiabatic to Zeno
• On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain
• Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
• On global approximate controllability of a quantum particle in a box by moving walls

Cited by in corpus (1)

• Global approximate controllability of quantum systems by form perturbations and applications