Particle Localization by Decoherence and Classical Lensing

Abstract

A phenomenological model of the time evolution of a particle wavepacket is presented that is subject to scattering event with small momentum transfer. It is suited for three dimensions and allows for an additional potential. For a random value of a phase parameter, it is equivalent to the decoherence by scattering off plane wave field states. Imposing some condition on the same phase parameter, the model delivers definite outcomes in a local pointer base. Common sense notions about the quantum-classical transition are readily obtained: Decoherent free particle solutions are localized constant-width wavepackets, quantum barrier scattering results in random reflection and transmission. The scattering process assumed in the phenomenological model is realized by scattering of a particle pair interacting by a force-distance law with small momentum transfer. Particles are localized not by decoherence but by a classical lensing effect. Schmidt paths in the Schmidt representation of the multiparticle state are products of single-particle wavepackets. Therefore the model has a natural 'Many Worlds' interpretation, identifying each Schmidt path with a classical branch. Different runs of the phenomenological model map the state of the same particular particle within different branches.