Energy Estimates for Low Regularity Bilinear Schrödinger Equations

2013/02/04 by Nabile Boussaïd, Nabile Boussaid, Marco Caponigro +4
Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics #math.OC

paper · pdf · doi:10.48550/arxiv.1302.0813

openalex publication_date 2013/02/04 · arxiv created 2013/02/07 · arxiv updated 2013/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with controls of bounded variation. Moreover, upper bounds of the error made when replacing the infinite dimensional system by its finite dimensional Galerkin approximations is presented.

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• Total Variation of the Control and Energy of Bilinear Quantum Systems
• Regular propagators of bilinear quantum systems
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• Implementation of logical gates on infinite dimensional quantum oscillators
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