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The theoretical description of materials' properties driven out ofequilibrium has important consequences in various fields such as semiconductorspintronics, nonlinear optics, continuous and discrete quantum informationscience and technology. The coupling of a quantum many-body system to anexternal bath can dramatically modify its dynamics compared to that of closedsystems, new phenomena like relaxation and decoherence appear as a consequenceof the nonunitary evolution of the quantum system. In addition,electron-electron correlations must be properly accounted for in order to gobeyond a simple one-electron or mean-field description of the electronicsystem. Here we discuss a first-principles methodology based on the evolutionof the electronic density matrix capable of treating electron-environmentinteractions and electron-electron correlations at the same level ofdescription. The effect of the environment is separated in a coherentcontribution, like the coupling to applied external electro-magnetic fields,and an incoherent contribution, like the interaction with lattice vibrations orthe thermal background of radiation. Electron-electron interactions areincluded using the nonequilibrium Green's function plus generalizedKadanoff-Baym ansatz. The obtained non-Markovian coupled set of equationsreduce to ordinary Lindblad quantum master equation form in the Markovianlimit.

First-principles open quantum dynamics for solids based on density-matrix formalism