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

publication date

  • October 2024

issue

  • 8

volume

  • 287

International Standard Serial Number (ISSN)

  • 0022-1236

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

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.

keywords

  • non-autonomous schrödinger equation; quantum control; stability; weak solutions