On the notion of ergodicity for finite quantum systems

We show that the orginal definition of ergodicity of Boltzmann can be directly applied to finite quantum systems, such as those arising from the quantization of classical systems on a compact phase space. It yields a notion of quantum ergodicity strictly stronger than the Von Neumann one. As an example, we remark that the quantized hyperbolic symplectomorphisms (a particular case is the quantized Arnold cat) are ergodic in this sense