Adiabatic control of the Schr\"odinger equation via conical intersections of the eigenvalues

TL;DR

This paper introduces a constructive adiabatic control method for the bilinear Schrödinger equation utilizing conical eigenvalue intersections, providing error estimates and applicable under generic spectral conditions.

Contribution

It presents a novel adiabatic control approach leveraging conical eigenvalue intersections, with explicit error bounds and broad applicability.

Findings

Control method effective for Hamiltonians with conical eigenvalue intersections

Provides sharp estimates relating control error to time

Applicable to generic spectral configurations

Abstract

In this paper we present a constructive method to control the bilinear Schr\"odinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if the latter are conical (as it happens generically). We provide sharp estimates of the relation between the error and the controllability time.