Localization by dissipative disorder: Deterministic approach to position measurements

We propose an approach to position measurements based on the hypothesis that the action of a position detector on a quantum system can be effectively described by a dissipative disordered potential. We show that such kind of potential is able, via the dissipation-induced Anderson localization, to contemporary localize the wave function of the system and to dissipate information to modes bounded to the detector. By imposing a diabaticity condition we demonstrate that the dissipative dynamics between the modes of the system leads to a localized energy exchange between the detector and the rest of the environment - the "click" of the detector - thus providing a complete deterministic description of a position measurement. We finally numerically demonstrate that our approach is consistent with the Born probability rule.