title: Irreversible quantum baker map.
abstract: We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet operator. A corresponding quantum system is constructed as a completely positive map acting in the space of density matrices. We investigate spectral properties of this superoperator and their link with the increase of the entropy of initially pure states.
authors.affiliation: Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland. lozinski@if.uj.edu.pl
authors.forename: Artur
authors.initials: A
authors.lastname: Łoziński
authors.forename: Prot
authors.initials: P
authors.lastname: Pakoński
authors.forename: Karol
authors.initials: K
authors.lastname: Zyczkowski