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There has been a very recent surge in the interest on the localizationproperties of resonances associated to partially open (scattering) systems,which are of great relevance when studying resonant cavities such as those usedin microlasers. Very recently, it has been found that no localization ispresent in a scaled form of these states. Moreover, a new kind of scarring onstructures different from periodic orbits is described for non scaledresonances. In this paper, we analyze the localization of a distributionfunction corresponding to the quantum LR representation -- based on the nonunitary evolution operator decomposition into left and right resonances -- forthe partially open quantum tribaker map, a paradigmatic system. We findlocalization on the shortest periodic orbits. Also, scaled states presentenhancements that could not be associated to periodic orbits and that becomemore evident when looking at the LR representation. These findings open thedoor for new perspectives on recent theoretical developments.

Average localization of resonances on the quantum repeller