First Principles Numerical Demonstration of Emergent Decoherent Histories

Abstract

Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schr\"odinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite size scaling law by varying the Hilbert space dimension over four orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework -- without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations, low-entropy initial states or ensemble averages.