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

• URL: http://arxiv.org/abs/2505.21017v1
• Date: Tue, 27 May 2025 10:50:02 GMT
• Title: Time-nonlocal versus time-local long-time extrapolation of non-Markovian quantum dynamics
• Authors: Moritz Cygorek, Erik M. Gauger,
• Abstract summary: We show that time-dependent time-local maps become stationary long before the open quantum system reaches its steady state.<n>Surprisingly, the maps become stationary long before the open quantum system reaches its steady state.<n>These results suggest that, perhaps counter-intuitively, time-nonlocality is not in fact a prerequiste for accurate and efficient long-time extrapolation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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