Quantum chaos in a two-level system in a semiclassical radiation field

Abstract

The semiclassical Bloch-Maxwell system is studied for chaos. Diagnostic criteria for chaos such as continuous power spectra and rapidly decaying correlations are shown not to be definitive. They may occur simultaneously with a vanishing maximum Liapunov exponent. The presence of a feedback effect on the radiation field is shown to lead to the possibility of bona fide chaos with a continuous spectrum and a positive Liapunov exponent. Whether or not chaos is exhibited in this system depends upon initial conditions as well, and cannot be deduced from the Hamiltonian alone.