Deterministic classical limit of the optimal control problem of quantum particles with spin

TL;DR

This paper investigates the classical limit of an optimal control problem for a quantum particle gas with spin, showing convergence from quantum to classical models using the Wigner formalism and phase-space trajectories.

Contribution

It proves the convergence of quantum optimal control solutions to a classical ODE-based model for particles with spin under spin-orbit coupling and magnetic fields.

Findings

Quantum solutions converge to classical trajectories in the limit

The classical control model simplifies the quantum problem

Validation of the classical limit in spin-dependent quantum systems

Abstract

We study the optimal control problem applied to a gas of particles with spin confined in a material with Rashba spin-orbit coupling effect, in the presence of an external magnetic field. The evolution of the particle gas is described in the Wigner formalism. We investigate the classical limit of the optimal control problem, and we prove the convergence of the solution of the quantum problem toward the solution of a simplified optimal control model, based on an ODE description of the particle gas in terms of a single spin vector traveling along a classical trajectory in the phase-space.