Non-Markovian Decoherence Times in Finite-Memory Environments

TL;DR

This paper develops a non-Markovian framework for decoherence in quantum systems with finite environmental memory, revealing that decoherence times scale with the square root of the correlation time and differ from entropy-based measures.

Contribution

It introduces a general time-nonlocal decoherence functional for finite-memory environments, explicitly recovering Markovian limits and analytically solving for Ornstein-Uhlenbeck environments.

Findings

Decoherence time scales as the square root of environmental correlation time.

Exponential decoherence only appears in the memoryless limit.

Decoherence rates can differ from entropy production indicators.

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.