A Description of Quantum Chaos

A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.