Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach

Abstract

Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent histories and Kolmogorov consistency. Second, the crucial role of quantum Markovianity (defined rigorously) to connect these concepts is established. Third, using a random matrix theory model, quantum effects are shown to be exponentially suppressed in the measurement statistics of slow and coarse observables despite the presence of large amount of coherences. This is also numerically exemplified, and it highlights the potential and importance of non-integrability and chaos for the emergence of classicality. Contents1 Introduction 2 2 Classicality: Definitions and approaches 3 2.1 Definition used in this work 3 2.2 The decoherence approach for open quantum systems 5 2.3 Consistent and decoherent histories 9 2.4 The new approach: General picture 10 3 Classicality: Derivation and numerical verification 13 3.1 Derivation using random matrix theory 13 3.2 Numerical verification 18 4 Conclusion 23 A Appendix 24 A.1 Decoherence, Markovianity and consistency 24 A.2 Numerical implementation 26 A.3 Higher order corrections 28 A.4 Trace distance bound under dephasing 30