The rolling sphere and the quantum spin

TL;DR

This paper explores the analogy between a rolling sphere on a curved surface and quantum spin precession, providing insights into geometrical phases in classical systems.

Contribution

It introduces a novel mapping between the classical rolling problem and quantum spin dynamics, aiding pedagogical understanding of geometrical phases.

Findings

Mapping reveals the connection between rolling motion and spin precession.

Provides a pedagogical framework for understanding geometrical phases.

Highlights the emergence of geometrical phases in classical mechanics.

Abstract

We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both rolling and spin precession, and in particular in understanding the emergence of geometrical phases in classical problems.