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

Baym, 1961, Conservation laws and correlation functions, Phys. Rev., 124, 287, 10.1103/PhysRev.124.287 Kadanoff, 2018 Keldysh, 1965, Diagram technique for nonequilibrium processes, Sov. Phys. JETP, 20, 1018 Fetter, 1971 Balzer, 2007 Stan, 2009, Time propagation of the Kadanoff-Baym equations for inhomogeneous systems, J. Chem. Phys., 130, 10.1063/1.3127247 Danielewicz, 1984, Quantum theory of nonequilibrium processes, I, Ann. Physics, 152, 239, 10.1016/0003-4916(84)90092-7 Bonitz, 1996, Numerical analysis of non-Markovian effects in charge-carrier scattering:One-time versus two-time kinetic equations, J. Phys.: Condens. Matter, 8, 6057 Hoppensteadt, 2007, Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels, BIT Numer. Math., 47, 325, 10.1007/s10543-007-0122-3 Kennedy, 2016 Kwong, 1998, Semiconductor Kadanoff-Baym equation results for optically excited electron–hole plasmas in quantum wells, Phys. Status Solidi (B), 206, 197, 10.1002/(SICI)1521-3951(199803)206:1<197::AID-PSSB197>3.0.CO;2-9 Kwong, 2000, Real-time Kadanoff-Baym approach to plasma oscillations in a correlated electron gas, Phys. Rev. Lett., 84, 1768, 10.1103/PhysRevLett.84.1768 Schlünzen, 2017, Comment on “on the unphysical solutions of the Kadanoff-Baym equations in linear response: Correlation-induced homogeneous density-distribution and attractors”, Phys. Rev. B, 96, 10.1103/PhysRevB.96.117101 Schlünzen, 2019, Ultrafast dynamics of strongly correlated fermions—nonequilibrium green functions and selfenergy approximations, J. Phys. Condens. Matter, 32, 10.1088/1361-648X/ab2d32 Von Friesen, 2009, Successes and failures of Kadanoff-Baym dynamics in hubbard nanoclusters, Phys. Rev. Lett., 103 Burton, 2005 Schmid, 2010, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech., 656, 5, 10.1017/S0022112010001217 Schmid, 2011, Application of the dynamic mode decomposition to experimental data, Exp. Fluids, 50, 1123, 10.1007/s00348-010-0911-3 Schmid, 2011, Applications of the dynamic mode decomposition, Theor. Comput. Fluid Dyn., 25, 249, 10.1007/s00162-010-0203-9 Schmid, 2012, Decomposition of time-resolved tomographic PIV, Exp. Fluids, 52, 1567, 10.1007/s00348-012-1266-8 Seena, 2011, Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations, Int. J. Heat Fluid Flow, 32, 1098, 10.1016/j.ijheatfluidflow.2011.09.008 Grosek, 2014 Kutz, 2015, Multi-resolution dynamic mode decomposition for foreground/background separation and object tracking, 921 Proctor, 2015, Discovering dynamic patterns from infectious disease data using dynamic mode decomposition, Int. Health, 7, 139, 10.1093/inthealth/ihv009 Yin, 2021 Kutz, 2016 Le Clainche, 2017, Higher order dynamic mode decomposition, SIAM J. Appl. Dyn. Syst., 16, 882, 10.1137/15M1054924 Tu, 2014, On dynamic mode decomposition: Theory and applications, J. Comput. Dyn., 1, 391, 10.3934/jcd.2014.1.391 Arbabi, 2017, Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator, SIAM J. Appl. Dyn. Syst., 16, 2096, 10.1137/17M1125236 Koopman, 1931, Hamiltonian systems and transformation in Hilbert space, Proc. Natl. Acad. Sci. USA, 17, 315, 10.1073/pnas.17.5.315 Koopman, 1932, Dynamical systems of continuous spectra, Proc. Natl. Acad. Sci. USA, 18, 255, 10.1073/pnas.18.3.255 Golub, 2013 Williams, 2015, A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition, J. Nonlinear Sci., 25, 1307, 10.1007/s00332-015-9258-5 Broomhead, 1986, Extracting qualitative dynamics from experimental data, Physica D, 20, 217, 10.1016/0167-2789(86)90031-X Packard, 1980, Geometry from a time series, Phys. Rev. Lett., 45, 712, 10.1103/PhysRevLett.45.712 Pan, 2020, On the structure of time-delay embedding in linear models of non-linear dynamical systems, Chaos, 30, 10.1063/5.0010886 Takens, 1981, Detecting strange attractors in turbulence, 366 Hubbard, 1963, Electron correlations in narrow energy bands, Proc. Math. Phys. Eng. Sci. P Royal Soc. A-Math. Phys., 276, 238 Tasaki, 1998, The Hubbard model-an introduction and selected rigorous results, J. Phys.: Condens. Matter, 10, 4353 White, 1989, Numerical study of the two-dimensional Hubbard model, Phys. Rev. B, 40, 506, 10.1103/PhysRevB.40.506 Lipavskỳ, 1986, Generalized Kadanoff-Baym ansatz for deriving quantum transport equations, Phys. Rev. B, 34, 6933, 10.1103/PhysRevB.34.6933 Hermanns, 2012, Non-equilibrium Green’s function approach to inhomogeneous quantum many-body systems using the generalized Kadanoff Baym Ansatz, Phys. Scr., 2012 Schlünzen, 2020, Achieving the scaling limit for nonequilibrium green functions simulations, Phys. Rev. Lett., 124, 10.1103/PhysRevLett.124.076601