Approximate controllability in small times of bilinear Schr{ö}dinger equations with magnetic drift
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917524713504768 |
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| author | Pozzoli, Eugenio |
| author_facet | Pozzoli, Eugenio |
| contents | We study the small-time approximate controllability of bilinear Schr{ö}dinger equations, where the drift is a magnetic Schr{ö}dinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in $\mathbb{R}^d$, with a quadratic and an additional generic bounded electric potential in the control, and with a uniform magnetic field in the drift; (ii) in $\mathbb{R}^d$ or $\mathbb{T}^d$, with control electric potentials supported on a finite number of Hermite or Fourier eigenfunctions, and with any differentiable magnetic potential in the drift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23665 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximate controllability in small times of bilinear Schr{ö}dinger equations with magnetic drift Pozzoli, Eugenio Analysis of PDEs Mathematical Physics Optimization and Control We study the small-time approximate controllability of bilinear Schr{ö}dinger equations, where the drift is a magnetic Schr{ö}dinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in $\mathbb{R}^d$, with a quadratic and an additional generic bounded electric potential in the control, and with a uniform magnetic field in the drift; (ii) in $\mathbb{R}^d$ or $\mathbb{T}^d$, with control electric potentials supported on a finite number of Hermite or Fourier eigenfunctions, and with any differentiable magnetic potential in the drift. |
| title | Approximate controllability in small times of bilinear Schr{ö}dinger equations with magnetic drift |
| topic | Analysis of PDEs Mathematical Physics Optimization and Control |
| url | https://arxiv.org/abs/2605.23665 |