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May 28, 20260 citationsOpen Access

Approximate controllability in small times of bilinear Schrödinger equations with magnetic drift

EPEugenio Pozzoli

Key Points

  • This research aims to explore the small-time approximate controllability of bilinear Schrödinger equations.
  • Analyzed bilinear Schrödinger equations in $ ext{R}^d$ with specific electric potentials and magnetic operators.
  • Proved controllability with uniform magnetic fields and bounded electric potential.
  • Investigated controllability with finite Hermite or Fourier eigenfunction supports under varying magnetic potentials.
  • Establish that controllability is achievable under defined conditions with quadratic electric potential.
  • Demonstrated approximate controllability with various differentiable magnetic potentials in finite eigenfunction scenarios.
  • Confirmed findings are valid for both $ ext{R}^d$ and $ ext{T}^d$ spaces.

Abstract

We study the small-time approximate controllability of bilinear Schrödinger equations, where the drift is a magnetic Schrödinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in Rᵈ, with a quadratic and an additional generic bounded electric potential in the control, and with a uniform magnetic field in the drift; (ii) in Rᵈ or Tᵈ, with control electric potentials supported on a finite number of Hermite or Fourier eigenfunctions, and with any differentiable magnetic potential in the drift.

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Cite This Study

Eugenio Pozzoli (2026) studied this question.

synapsesocial.com/papers/6a17daf83fad632b0f9d7cd7https://doi.org/10.48550/arxiv.2605.23665
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