Non-Markovian Decoherence Times in Finite-Memory Environments

TL;DR

The paper reframes decoherence in open quantum systems by introducing a general time-nonlocal decoherence functional dependent on the environmental force correlation function. It shows that for any finite environmental memory, coherence decays quadratically at short times, yielding a decoherence time $\tau_{\mathrm{dec}}$ that scales as $\sqrt{\tau_c}$, with Markovian exponential decay arising only as a singular limit when memory vanishes. Analytic results are provided for Gaussian, soft power-law, and Ornstein-Uhlenbeck baths, with exact numerical validation for the OU case via a pseudomode mapping, and consistency with HEOM. The work also clarifies that decoherence rates do not directly equal observable loss of quantum signatures (purity and entropy can evolve on different timescales) and introduces an inferred-memory viewpoint where bath memory time is extracted from data. These insights offer a model-agnostic framework for diagnosing non-Markovian memory in engineered and biological-like environments and guiding memory-aware control of open quantum systems.

Abstract

Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence and are frequently used as effective bounds on quantum behavior in complex environments. Such descriptions, however, correspond to the singular physical limit of vanishing environmental memory. Here we formulate decoherence using a general time-nonlocal decoherence functional determined solely by the environmental force correlation function, with Markovian dynamics recovered explicitly as a limiting case. For arbitrary stationary environments with finite temporal correlations, we show that the decoherence functional exhibits quadratic short-time growth that is model-independent within the finite-memory class considered. Consequently, the decoherence time defined operationally-without assuming exponential decay-scales as the square root of the environmental correlation time, independent of the detailed form of the bath correlation kernel. These results are illustrated analytically for Gaussian-correlated, soft power-law, and Ornstein-Uhlenbeck environments. In the Ornstein-Uhlenbeck case, the non-Markovian dynamics admit an exact analytical closure, yielding a closed evolution equation for the coherence. Exact numerical simulations based on a pseudomode mapping confirm the predicted scaling and show that exponential decoherence emerges only in the memoryless limit. Beyond coherence decay, we distinguish decoherence rates from observable loss of quantum signatures by analyzing purity and von Neumann entropy dynamics. We show that suppression of a specific coherence element need not coincide with irreversible entropy production. Finally, we introduce an inferred-memory perspective in which the environmental correlation time is treated as an operationally extractable parameter from dynamical data.

Figures (2)

• Figure 1: Decoherence time $\tau_{\mathrm{dec}}$ extracted from pseudomode simulations as a function of bath correlation time $\tau_c$. The dashed line indicates the $\sqrt{\tau_c}$ scaling predicted analytically.(Data and simulation parameters as in Ref. Dewan2026FiniteMemoryBio; shown here to illustrate the generalized finite-memory scaling discussed in the present work.)
• Figure 2: Representative coherence decay curves $C(t)$ obtained from exact pseudomode simulations for different bath correlation times $\tau_c$. For all finite $\tau_c$, the coherence exhibits a quadratic short-time decay, in contrast with the exponential behaviour predicted by the Markovian approximation.(Data and simulation parameters as in Ref. Dewan2026FiniteMemoryBio; shown here to illustrate the generalized finite-memory scaling discussed in the present work.)