Magnetic operations: a little fuzzy physics?

TL;DR

This paper explores the behavior of charged particles in magnetic fields, highlighting the quantum 'fuzzy point' concept and its implications for magnetic control beyond traditional quantum Hall effects.

Contribution

It introduces the idea of a 'fuzzy point' in quantum particle trajectories and demonstrates its relevance to magnetic control in oscillating fields.

Findings

Fuzzy point concept extends non-commutative geometry in magnetic fields.

Magnetic control maps differ from traditional Strutt diagrams in oscillating fields.

Quantum effects influence stability regions in magnetic control scenarios.

Abstract

We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.