Decoherence of Histories: Chaotic Versus Integrable Systems

TL;DR

This study investigates how the nature of quantum systems, whether chaotic or integrable, influences the emergence of decoherence in isolated systems, highlighting the role of chaos in classicality emergence.

Contribution

It provides a numerical analysis of decoherence in different quantum systems, revealing the impact of chaos versus integrability on coherence suppression over time.

Findings

Strong exponential suppression of coherences in chaotic systems

Weak exponential suppression in interacting integrable systems

No exponential suppression in non-interacting integrable systems

Abstract

We study the emergence of decoherent histories in isolated systems based on exact numerical integration of the Schr\"odinger 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) non-interacting integrable, strongly impacts decoherence \new{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) time scale. 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 time scales. This behaviour is encoded in the multi-time 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.