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arXiv:2509.00845

Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables

Nataliya Arefyeva, Evgeny Polyakov

Published Aug 31, 2025• 0 citations
arXivHTMLPDF

Abstract

We propose a new approach to coarse-grained description of quantum evolution that provides an explicit recipe to construct and evaluate multi-time decoherent histories in a controlled way, applicable to non-Markovian and integrable systems. Specifically, we study local interaction quench of a local degree of freedom (an open quantum system) within a noninteracting integrable environment. This setting allows us to identify the environmental degrees of freedom that irreversibly store records of the system's past. These modes emerge sequentially in time and define the projectors required for decoherent histories. We show numerically that the off-diagonal elements of the decoherence functional are exponentially suppressed relative to a significance threshold.

DOI
10.48550/arxiv.2509.00845

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We propose a new approach to coarse-grained description of quantum evolution that provides an explicit recipe to construct and evaluate multi-time decoherent histories in a controlled way, applicable to non-Markovian and integrable systems. Specifically, we study local interaction quench of a local degree of freedom (an open quantum system) within a noninteracting integrable environment. This setting allows us to identify the environmental degrees of freedom that irreversibly store records of the system's past. These modes emerge sequentially in time and define the projectors required for decoherent histories. We show numerically that the off-diagonal elements of the decoherence functional are exponentially suppressed relative to a significance threshold.
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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.
We study the decoherence properties of a certain class of Markovian quantum open systems from both the Decohering Histories and Environment Induced Superselection paradigms. The class studied includes many familiar quantum optical cases. For this class, we show that there always exists a basis which leads to {\em exactly} consistent histories for any coarse graining {\em irrespective} of the initial conditions. The magnitude of the off--diagonal elements of the reduced density matrix ρρρ in this basis however, depends on the initial conditions. Necessary requirements for classicality as advanced by the two paradigms are thus in direct conflict in these systems.
We propose an effective field-theoretic framework for open quantum systems in which decoherence dynamics are influenced by an auxiliary scalar field acting as an informational memory degree of freedom. This additional field induces intrinsically non-Markovian behavior, leading to structured noise spectra and deviations from standard exponential decay. The resulting reduced dynamics are governed by a non-local memory kernel, capturing temporal correlations beyond conventional approaches. We show that the model predicts oscillatory modulations in coherence decay and provides improved fits to simulated qubit data compared to both exponential and stretched-exponential models. The framework also reproduces nontrivial residual structures and spectral features that are not accounted for in standard decoherence theories. To test these predictions, we propose an experimental protocol using superconducting qubits, where systems initialized under identical environmental conditions but with different controlled histories exhibit distinguishable decoherence dynamics. This history dependence offers a potential experimental signature of the proposed mechanism. Overall, this work provides a phenomenological extension of decoherence theory and highlights the role of memory effects and informational degrees of freedom in open quantum systems, suggesting new directions for both theoretical and experimental investigation.
In the context of the decoherent histories approach to quantum theory, we investigate the idea that decoherence is connected with the storage of information about the decohering system somewhere in the universe. The known connection between decoherence and the existence of records is extended from the case of pure initial states to mixed states, where it is shown that records may still exist but are necessarily imperfect. We formulate an information-theoretic conjecture about decoherence due to an environment; the number of bits required to describe a set of decoherent histories is approximately equal to the number of bits of information thrown away to the environment in the coarse-graining process. This idea is verified in a simple model consisting of a particle coupled to an environment that can store only one bit of information. We explore the decoherence and information storage in the quantum Brownian motion model, in which a particle trajectory is decohered as a result of coupling to an environment of harmonic oscillators in a thermal state. It is shown that the variables that the environment naturally measures and stores information about are nonlocal functions of time, which are essentially the Fourier components of the function x(t)x(t)x(t) (describing the particle trajectory). In particular, the records storing the information about the Fourier modes are the positions and momenta of the environmental oscillators at the final time. We show that it is possible to achieve decoherence even if there is only one oscillator in the environment. The information count of the histories and records in the environment adds up according to our conjecture. These results give quantitative content to the idea that decoherence is related to ``information lost.'' Some implications of these ideas for quantum cosmology are discussed.