Real-time dynamics of spins coupled to a conduction-electron system ; Realzeitdynamik von an Leitungselektronen gekoppelten Spins

The static hybridization mean-field (HybMF) approach is generalized to the nonequilibrium case for Kondo systems by employing the non-equilibrium perturbation theory for Keldysh-Matsubara Green’s functions. This time-dependent hybridization mean-field (tHybMF) is a conserving approximation, readily accessible by Runge-Kutta methods and can be generally used to address various problems concerning Kondo systems far from thermal equilibrium, such as time-dependent Kondo screening as well as the time-dependent competition of the Kondo effect with the Ruderman-Kittel-Kasuya-Yosida indirect magnetic exchange interaction. Another line of research comprises the Kondo model as a paradigmatic system to study the longitudinal and transversal dynamics of spins coupled to a conduction-electron system, which will be in the focus of the present work. Here, the equations of motion for charge, hybridization and spins are derived. Subsequently, the focus is set on the transversal spin dynamics, which appears to be a more classical phenomenon, and relations to previous approaches to classical spin dynamics such as the quantum-classical hybrid method and the linear-response spin dynamics are established. In addition the Landau-Lifshitz-Gilbert equation and in particular the Gilbert-damping term is re-derived revealing that this concept is ill-defined for the case of a non-interacting one-dimensional system. Moreover, a numerical study of the real-time dynamics of a classical spin subject to an external magnetic field and locally exchange coupled to a one-dimensional system of conduction electrons is performed. It is shown, that (i) the relaxation of the spin results from retardation effects in the coupled electron-spin dynamics; (ii) as total energy and spin are conserved in the relaxation process, energy and spin carried by dispersive wave packets of excitations are dissipated into the bulk of the system; (iii) in contrast to the classical theory, the nutational motion of a quantum spin is efficiently damped on a femtosecond time ...