Stability and control of a 1D quantum system with confining time dependent delta potentials
Analysis of PDEs
2015-05-19 v3 Mathematical Physics
math.MP
Optimization and Control
Abstract
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the Hamiltonian, we prove the existence of strict solutions to the corresponding Schr\"odinger equation. The result is used to discuss the stability and the steady-state local controllability of the wavefunction when the strenght of the interaction is used as a control parameter.
Cite
@article{arxiv.1006.3329,
title = {Stability and control of a 1D quantum system with confining time dependent delta potentials},
author = {Andrea Mantile},
journal= {arXiv preprint arXiv:1006.3329},
year = {2015}
}
Comments
latex, 21 pages, title changed