Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems

2019/09/05 by Augier, Nicolas, Boscain, Ugo, Sigalotti, Mario · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1909.02271

Abstract

We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical intersections of eigenvalues. Then, through the use of normal forms, we study the problem of ensemble controllability between the eigenstates of a generic Hamiltonian.

Cited by

• An approach to control design for two-level quantum ensemble systems

Related

• Quantum subspace controllability implying full controllability
• A Sufficient Condition for Partial Ensemble Controllability of Bilinear Schrödinger Equations with Bounded Coupling Terms
• Control of non-controllable quantum systems: a quantum control algorithm based on Grover iteration
• Schrödinger eigenfunctions sharing the same modulus and applications to the control of quantum systems
• Controllability of Scattering States of Quantum Mechanical Systems