Decoherence induced by a chaotic environment: A quantum walker with a complex coin

We study the differences between the process of decoherence induced by chaotic and regular environments. For this we analyze a family of simple models wich contain both regular and chaotic environments. In all cases the system of interest is a "quantum walker", i.e. a quantum particle that can move on a lattice with a finite number of sites. The walker interacts with an environment wich has a D dimensional Hilbert space. The results we obtain suggest that regular and chaotic environments are not distinguishable from each other in a (short) timescale t*, wich scales with the dimensionality of the environment as t*~log(D). Howeber, chaotic environments continue to be effective over exponentially longer timescales while regular environments tend to reach saturation much sooner. We present both numerical and analytical results supporting this conclusion. The family of chaotic evolutions we consider includes the so-called quantum multi-baker-map as a particular case.