Compact and complete description of non-Markovian dynamics

TL;DR

This paper shows how the time-convolutionless formalism offers a compact, complete, and physically interpretable way to describe non-Markovian dynamics, simplifying analysis and computation in complex quantum and biological systems.

Contribution

It demonstrates the construction and analysis of the time-local generator from reference dynamics, highlighting its advantages over traditional nonlocal approaches.

Findings

Time-local approach provides a more compact description.

The method simplifies the analysis of non-Markovian dynamics.

A protocol for discrete-time application is introduced.

Abstract

Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices, to qubit decoherence in quantum technologies, and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analogue and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.