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Time-dependent many-body treatment of electron-boson dynamics: application to plasmon-accompanied photoemission

Recent experiments access the time-resolved photoelectron signal originating from plasmon satellites in correlated materials and address their build-up and decay in real time. Motivated by these developments, we present the Kadanoff-Baym formalism for the nonequilibrium time evolution of interacting fermions and bosons. In contrast to the fermionic case the bosons are described by second-order differential equations. Solution of the bosonic Kadanoff-Baym equations - which is the central ingredient of this work - requires substantial modification of the usual two-times electronic propagation scheme. The solution is quite general and can be applied to a number of problems, such as the interaction of electrons with quantized photons, phonons and other bosonic excitations. Here, the formalism is applied to the photoemission from a deep core hole accompanied by plasmon excitation. We compute the time-resolved photoelectron spectra and discuss the effects of intrinsic and extrinsic electron energy losses and their interference.