Tunable Lyapunov exponent in inverse magnetic billiards
arXiv:cond-mat/0208491 · doi:10.1103/PhysRevE.67.065202
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.
4 pages, 6 figures
References in corpus (8)
- Quantum Transport in Semiconductor Nanostructures
- Chaos in Andreev Billiards
- Unstable Periodic Orbits in the Stadium Billiard
- A magnetic barrier in confined two-dimensional electron gases: Nanomagnetometers and magnetic switches
- Electron scattering on circular symmetric magnetic profiles in a two-dimensional electron gas
- Non-homogeneous magnetic field induced magnetic edge states and their transport in a quantum wire
- Hyperbolic Billiards on Surfaces of Constant Curvature
- Hyperbolic Magnetic Billiards on Surfaces of Constant Curvature
Cited by in corpus (8)
- Estimating Lyapunov exponents in billiards
- Quantum and semiclassical study of magnetic anti-dots
- Billiards in magnetic fields: A molecular dynamics approach
- On the Dynamics of Inverse Magnetic Billiards
- Current distribution in magnetically confined 2DEG: semiclassical and quantum mechanical treatment
- Recovering Obstacles from their Travelling Times
- Linear Stability of Periodic Trajectories in Inverse Magnetic Billiards
- Inverse-Magnetic Billiards on a Square