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Interacting electrons and bosons in the doubly screened <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mover accent="true"><mml:mi>W</mml:mi><mml:mo>̃</mml:mo></mml:mover></mml:mrow></mml:math> approximation: A time-linear scaling method for first-principles simulations

Interacting electrons and bosons in the doubly screened <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mover accent="true"><mml:mi>W</mml:mi><mml:mo>̃</mml:mo></mml:mover></mml:mrow></mml:math> approximation: A time-linear scaling method for first-principles simulations

We augment the time-linear formulation of the Kadanoff-Baym equations for systems of interacting electrons and quantized phonons or photons with the $G\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ approximation, the Coulomb interaction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ being dynamically screened by both electron-hole pairs and bosonic particles. We also show how to combine different approximations to …