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arXiv · 2211.05868

Dynamic Mode Decomposition for Extrapolating Non-equilibrium Green's Functions Dynamics

Cian C. Reeves·Jia Yin·Yuanran Zhu·Khaled Z. Ibrahim·Chao Yang·Vojtech Vlcek
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Abstract

The HF-GKBA offers an approximate numerical procedure for propagating the two-time non-equilibrium Green's function(NEGF). Here we compare the HF-GKBA to exact results for a variety of systems with long and short-range interactions, different two-body interaction strengths and various non-equilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. This agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, look at the use of dynamical mode decomposition(DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16\% of the total time evolution we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long time trajectories in large-scale systems.

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Cian C. Reeves, Jia Yin, Yuanran Zhu, Khaled Z. Ibrahim, Chao Yang, Vojtech Vlcek. 2023-01-20. Dynamic Mode Decomposition for Extrapolating Non-equilibrium Green's Functions Dynamics. https://doi.org/10.1103/physrevb.107.075107

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