Tunable Lyapunov exponent in inverse magnetic billiards

TL;DR

This paper studies how the stability and chaos of charged particle trajectories in a stadium-shaped inverse magnetic domain can be smoothly controlled by adjusting the external magnetic field, revealing tunable Lyapunov exponents.

Contribution

It introduces a novel method for numerically measuring Lyapunov exponents and demonstrates how the phase space structure can be continuously tuned via magnetic field strength.

Findings

Lyapunov exponent varies smoothly with magnetic field

Phase space transitions from ergodic to mixed states

Potential for experimental realization of tunable chaos

Abstract

The stability properties of the classical trajectories of charged particles are investigated in a two dimensional stadium-shaped inverse magnetic domain, where the magnetic field is zero inside the stadium domain and constant outside. In the case of infinite magnetic field the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (performed with a novel method) and the integrable/chaotic phase space volume ratio show that both quantities can be smoothly tuned by varying the external magnetic field. A possible experimental realization of the arrangement is also discussed.