DYNAMICS OF A CHARGED-PARTICLE IN A MAGNETIC-FLUX LATTICE

The dynamics of a charged particle in a two-dimensional space under th e influence of a nonuniform, periodic magnetic field, similar to the m agnetic induction inside an extremely type-II superconductor in the vo rtex state, is studied. The Hamiltonian for this model is found to be classically nonintegrable. A study of classical trajectories shows a g lobal transition from a confined chaotic motion on tori for small ampl itude of the periodic modulation, to an extended chaotic system that f ills phase space uniformly, for strong modulations. The classical dyna mics is confronted with a semiclassical Gaussian wave-packet approach and a time-dependent quantum-mechanical (QM) propagation scheme, for t he same Hamiltonian. When the magnetic field modulation is small the e nvelopes of both the semiclassical and the exact QM autocorrelation fu nctions are found to be Gaussian at short times. For a strong magnetic field modulation the envelope of the semiclassical autocorrelation fu nction crosses over to a decaying exponential, determined by the chara cteristic Lyapunov exponent of the chaotic motion. It deviates signifi cantly from the exact QM autocorrelation function, which retains the G aussian envelope. The relatively strong recursion peaks of the latter may indicate a quantum localization effect.