Quantum dynamics of a two-level system coupled to a bosonic degree of freedom in terms of Wigner phase space distributions

Abstract

The quantum dynamics of the Hamiltonian of a two-level system coupled to a boson mode is formulated in terms of the Wigner matrix. The trace of the Wigner matrix gives complete information for the bosonic degree of freedom. The time evolution and the long time average of the trace of the Wigner matrix is calculated numerically for small perturbations and in resonance. Some aspects of 'quantum chaos' of the two-level system are discussed.