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arXiv · 2203.14892

Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green's function

Jia Yin·Yang-hao Chan·Felipe da Jornada·Diana Qiu·Steven G. Louie·Chao Yang
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Abstract

Computing the numerical solution of the Kadanoff-Baym equations, a set of nonlinear integral differential equations satisfied by two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solution of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. We partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonls of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. We demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

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Jia Yin, Yang-hao Chan, Felipe da Jornada, Diana Qiu, Steven G. Louie, Chao Yang. 2022-03-28. Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green's function. https://arxiv.org/abs/2203.14892

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