General Approach to the Quantum Kicked Particle in a Magnetic Field: Quantum-Antiresonance Transition

Abstract

The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for {\em general} values of the conserved coordinate $x_{\rm c}$ of the cyclotron orbit center. The system exhibits spectral structures [``Hofstadter butterflies'' (HBs)] and quantum diffusion depending sensitively on $x_{\rm c}$. Most significant changes take place when $x_{\rm c}$ approaches the value at which quantum antiresonance (exactly periodic recurrences) can occur: the HB essentially ``doubles'' and the quantum-diffusion coefficient $D(x_{\rm c})$ is strongly reduced. An explanation of these phenomena, including an approximate formula for $D(x_{\rm c})$ in a class of wave packets, is given on the basis of an effective Hamiltonian which is derived as a power expansion in a small parameter. The global quantum diffusion of a two-dimensional wave packet for all $x_{\rm c}$ is briefly considered.