Time-nonlocal versus time-local long-time extrapolation of non-Markovian quantum dynamics

TL;DR

This paper compares time-nonlocal and time-local methods for extrapolating long-time dynamics in non-Markovian quantum systems, finding that simpler time-local approaches are equally effective and often faster.

Contribution

It demonstrates that time-local extrapolation can replace time-nonlocal methods for long-time quantum dynamics prediction, simplifying the process.

Findings

Time-local maps become stationary before steady state.

Both methods converge with longer short-time propagation.

Time-local extrapolation is at least as fast as time-nonlocal.

Abstract

The high numerical demands for simulating non-Markovian open quantum systems motivate a line of research where short-time dynamical maps are extrapolated to predict long-time behavior. The transfer tensor method (TTM) has emerged as a powerful and versatile paradigm for such scenarios. It relies on a systematic construction of a converging sequence of time-nonlocal corrections to a time-constant local dynamical map. Here, we show that the same objective can be achieved with time-local extrapolation based on the observation that time-dependent time-local dynamical maps become stationary. Surprisingly, the maps become stationary long before the open quantum system reaches its steady state. Comparing both approaches numerically on examples of the canonical spin-boson model with sub-ohmic, ohmic, and super-ohmic spectral density, respectively, we find that, while both approaches eventually converge with increasing length of short-time propagation, our simple time-local extrapolation invariably converges at least as fast as time-nonlocal extrapolation. These results suggest that, perhaps counter-intuitively, time-nonlocality is not in fact a prerequiste for accurate and efficient long-time extrapolation of non-Markovian quantum dynamics.