Decoherence of Histories: Chaotic Versus Integrable Systems

We study the emergence of decoherent histories in isolated systems based on exact numerical integration of the Schrödinger equation for a Heisenberg chain. We reveal that the nature of the system, which we switch from (i) chaotic to (ii) interacting integrable to (iii) noninteracting integrable, strongly impacts decoherence of coarse spin observables. From a finite size scaling law we infer a strong exponential suppression of coherences for (i), a weak exponential suppression for (ii), and no exponential suppression for (iii) on a relevant short (nonequilibrium) timescale. Moreover, for longer times we find stronger decoherence for (i) but the opposite for (ii), hinting even at a possible power-law decay for (ii) at equilibrium timescales. This behavior is encoded in the multitime properties of the quantum histories and it can not be explained by environmentally induced decoherence. Our results suggest that chaoticity plays a crucial role in the emergence of classicality in finite size systems.