Tunable Lyapunov exponent in inverse magnetic billiards

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.