\begin{pseudochapter}{Abstract}

The search and characterisation of new quantum phases of matter has recently been intensified by the application of terahertz (THz) spectroscopy in the time domain to heavy-fermion systems. It was experimentally shown that a single-cycle THz pulse disrupts the strongly interacting Kondo regime of heavy-fermion compounds such as CeCu$_{6-x}$Au$_{x}$, which recover after a characteristic delay time, accompanied by the emission of a temporally confined THz echo. The transient nature of such non-equilibrium dynamics leads to new and exciting many-body physics, raising questions about the established properties of quasiparticles. 

In this thesis, the theoretical description of these heavy-fermion non-equilibrium dynamics is developed. The electronic part of the system is captured by an Anderson lattice model and described by non-equilibrium dynamical mean-field theory and the non-crossing approximation. Such heavy-fermion systems already constitute a challenging problem in thermal equilibrium due to the electronic and spin degrees of freedom being fundamentally entangled. The non-equilibrium drive is a quantised Gaussian pulse of THz light coupled to the heavy-fermion system by a dipole interaction. The release of excess energy during the relaxation dynamics following excitation is treated beyond the typical Markovian master equation, with relaxation to ambient temperature possible via radiative recombination and electronic particle-exchange channels. The long-time dynamics associated with the driven-dissipative strongly-interacting lattice system are resolved at the level of two-point functions via an adaptive algorithm, and temporal aspects regarding the revival of the Kondo regime following its destruction by the pulse of radiation are discussed.

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