Quantum iterated function systems

Artur Łoziński, Karol Życzkowski, Wojciech Słomczyński
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal
more » ... ucture, and study properties of the corresponding QIFSs and their invariant states.
doi:10.1103/physreve.68.046110 pmid:14683005 fatcat:jifyvpfn3rexvp6b3zld632mbq