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

Yin, Jia; Chan, Yang-hao; Jornada, Felipe da; Qiu, Diana Y.; Louie, Steven G.; Yang, Chao

doi:10.1016/j.jocs.2022.101843

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

Journal Article · Tue Sep 06 00:00:00 EDT 2022 · Journal of Computational Science

DOI:https://doi.org/10.1016/j.jocs.2022.101843· OSTI ID:2278658

^[1]; Chan, Yang-hao ^[2]; Jornada, Felipe da ^[3]; Qiu, Diana Y. ^[4]; Louie, Steven G. ^[5]; Yang, Chao ^[1]

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Applied Mathematics & Computational Research Division
Academia Sinica, Taipei (Taiwan)
Stanford University, CA (United States)
Yale University, New Haven, CT (United States)
University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Materials Sciences Division

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the 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 solutions 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 subdiagonals 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. In conclusion, we demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 2278658

Alternate ID(s):: OSTI ID: 1962157

Journal Information:: Journal of Computational Science, Vol. 64; ISSN 1877-7503

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (26)

Comment on “On the unphysical solutions of the Kadanoff-Baym equations in linear response: Correlation-induced homogeneous density-distribution and attractors” Schlünzen, N.; Joost, J. -P.; Bonitz, M. Physical Review B, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevB.96.117101	journal	September 2017
Ultrafast dynamics of strongly correlated fermions—nonequilibrium Green functions and selfenergy approximations Schlünzen, N.; Hermanns, S.; Scharnke, M. Journal of Physics: Condensed Matter, Vol. 32, Issue 10 https://doi.org/10.1088/1361-648X/ab2d32	journal	December 2019
Application of the dynamic mode decomposition to experimental data Schmid, Peter J. Experiments in Fluids, Vol. 50, Issue 4 https://doi.org/10.1007/s00348-010-0911-3	journal	February 2011
Dynamic mode decomposition of numerical and experimental data Schmid, Peter J. Journal of Fluid Mechanics, Vol. 656 https://doi.org/10.1017/S0022112010001217	journal	July 2010
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W. Journal of Nonlinear Science, Vol. 25, Issue 6 https://doi.org/10.1007/s00332-015-9258-5	journal	June 2015
Generalized Kadanoff-Baym ansatz for deriving quantum transport equations Lipavský, P.; Špička, V.; Velický, B. Physical Review B, Vol. 34, Issue 10 https://doi.org/10.1103/PhysRevB.34.6933	journal	November 1986
Geometry from a Time Series Packard, N. H.; Crutchfield, J. P.; Farmer, J. D. Physical Review Letters, Vol. 45, Issue 9 https://doi.org/10.1103/PhysRevLett.45.712	journal	September 1980
Semiconductor Kadanoff-Baym Equation Results for Optically Excited Electron-Hole Plasmas in Quantum Wells Kwong, N. H.; Bonitz, M.; Binder, R. physica status solidi (b), Vol. 206, Issue 1 https://doi.org/10.1002/(SICI)1521-3951(199803)206:1<197::AID-PSSB197>3.0.CO;2-9	journal	March 1998
Hamiltonian Systems and Transformation in Hilbert Space Koopman, B. O. Proceedings of the National Academy of Sciences, Vol. 17, Issue 5 https://doi.org/10.1073/pnas.17.5.315	journal	May 1931
Time propagation of the Kadanoff–Baym equations for inhomogeneous systems Stan, Adrian; Dahlen, Nils Erik; van Leeuwen, Robert The Journal of Chemical Physics, Vol. 130, Issue 22 https://doi.org/10.1063/1.3127247	journal	June 2009
Quantum theory of nonequilibrium processes, I Danielewicz, P. Annals of Physics, Vol. 152, Issue 2 https://doi.org/10.1016/0003-4916(84)90092-7	journal	February 1984
Numerical study of the two-dimensional Hubbard model White, S. R.; Scalapino, D. J.; Sugar, R. L. Physical Review B, Vol. 40, Issue 1 https://doi.org/10.1103/PhysRevB.40.506	journal	July 1989
Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels Hoppensteadt, F. C.; Jackiewicz, Z.; Zubik-Kowal, B. BIT Numerical Mathematics, Vol. 47, Issue 2 https://doi.org/10.1007/s10543-007-0122-3	journal	March 2007
Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations Seena, Abu; Sung, Hyung Jin International Journal of Heat and Fluid Flow, Vol. 32, Issue 6 https://doi.org/10.1016/j.ijheatfluidflow.2011.09.008	journal	December 2011
Conservation Laws and Correlation Functions Baym, Gordon; Kadanoff, Leo P. Physical Review, Vol. 124, Issue 2 https://doi.org/10.1103/PhysRev.124.287	journal	October 1961
Higher Order Dynamic Mode Decomposition Le Clainche, Soledad; Vega, José M. SIAM Journal on Applied Dynamical Systems, Vol. 16, Issue 2 https://doi.org/10.1137/15M1054924	journal	January 2017
Real-Time Kadanoff-Baym Approach to Plasma Oscillations in a Correlated Electron Gas Kwong, N. -H.; Bonitz, M. Physical Review Letters, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevLett.84.1768	journal	February 2000
Extracting qualitative dynamics from experimental data Broomhead, D. S.; King, Gregory P. Physica D: Nonlinear Phenomena, Vol. 20, Issue 2-3 https://doi.org/10.1016/0167-2789(86)90031-X	journal	June 1986
On the structure of time-delay embedding in linear models of non-linear dynamical systems Pan, Shaowu; Duraisamy, Karthik Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, Issue 7 https://doi.org/10.1063/5.0010886	journal	July 2020
Dynamical Systems of Continuous Spectra Koopman, B. O.; Neumann, J. v. Proceedings of the National Academy of Sciences, Vol. 18, Issue 3 https://doi.org/10.1073/pnas.18.3.255	journal	March 1932
On dynamic mode decomposition: Theory and applications Kutz, J. Nathan; Brunton, Steven L.; Luchtenburg, Dirk M. Journal of Computational Dynamics, Vol. 1, Issue 2 https://doi.org/10.3934/jcd.2014.1.391	journal	December 2014
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator Arbabi, Hassan; Mezić, Igor SIAM Journal on Applied Dynamical Systems, Vol. 16, Issue 4 https://doi.org/10.1137/17M1125236	journal	January 2017
Decomposition of time-resolved tomographic PIV Schmid, Peter J.; Violato, Daniele; Scarano, Fulvio Experiments in Fluids, Vol. 52, Issue 6 https://doi.org/10.1007/s00348-012-1266-8	journal	February 2012
Applications of the dynamic mode decomposition Schmid, P. J.; Li, L.; Juniper, M. P. Theoretical and Computational Fluid Dynamics, Vol. 25, Issue 1-4, p. 249-259 https://doi.org/10.1007/s00162-010-0203-9	journal	August 2010
Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations Schlünzen, Niclas; Joost, Jan-Philip; Bonitz, Michael Physical Review Letters, Vol. 124, Issue 7 https://doi.org/10.1103/PhysRevLett.124.076601	journal	February 2020
Discovering dynamic patterns from infectious disease data using dynamic mode decomposition Proctor, Joshua L.; Eckhoff, Philip A. International Health, Vol. 7, Issue 2 https://doi.org/10.1093/inthealth/ihv009	journal	February 2015

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