Does quantum chaos exist? (A quantum Lyapunov exponents approach.)
  We shortly review the progress in the domain of deterministic chaos for quantum dynamical systems. With the appropriately extended definition of quantum Lyapunov exponent we analyze various quantum dynamical maps. It is argued that, within Quantum Mechanics, irregular evolution for properly chosen observables can coexist with regular and predictable evolution of states. 
W. A. Majewski