On Global Approximate Controllability of a Quantum Particle in a Box by Moving Walls Articles uri icon

publication date

  • March 2024

start page

  • 826

end page

  • 852

issue

  • 2

volume

  • 62

International Standard Serial Number (ISSN)

  • 0363-0129

Electronic International Standard Serial Number (EISSN)

  • 1095-7138

abstract

  • We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system: any initial pure state can be driven arbitrarily close to any target pure state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schrödinger equation and use a stability theorem for the time-dependent Schrödinger equation.

subjects

  • Mathematics

keywords

  • quantum control; approximate controllability; infinite-dimensional systems; quantum particle; moving walls