Localisation of a wave-function by superposition of different histories

Abstract

Quantum state diffusion shows how stochastic interaction with the environment may cause localisation of the wave-function, and thereby demonstrates that quantum mechanics need not invoke a separate axiom of measurement to explain the emergence of the classical world. It has not been clear whether quantum state diffusion requires some new physics. We set up an explicit numerical calculation of the evolution of the wave-function of a two-state system under interaction using only the physics explicitly contained in quantum mechanics without an axiom of measurement. The wave-function does indeed localise, as proposed by quantum state diffusion, on eigenstates of the perturbation. The mechanism appears to be the superposition of histories evolving under different Hamiltonians.