The origin of the Mixed Glass Former Effect (MGFE) is studied, which manifests itself in a non-monotonic behavior of the activation energy for long-range ion transport as a function of the mixing ratio of two glass formers. Two theoretical models are developed, the mixed barrier model and the network unit trap model, which consider different possible mechanisms for the occurrence of the MGFE. The mixed barrier model is based on the assumption that energy barriers are reduced for ionic jumps in regions of mixed composition. By employing percolation theory it is shown that this mechanism can successfully account for the behavior of the activation energy in various ion conducting mixed glass former glasses. The network unit trap model is based on the fact that a variety of network forming units, the so-called Q(n) species, can be associated with one glass former. Using a thermodynamic approach, the change of the concentration of these units in dependence of ionic concentration and the glass former mixing ratio is successfully predicted for alkali borate, phosphate and borophosphate glasses. In a second step, the charge distribution of the various units is considered and related to it, the binding energies to alkali ions. This gives rise to a modeling of the ionic transport in an energy landscape that changes in a defined manner with the glass former mixing ratio. Kinetic Monte Carlo simulations for alkali borophosphate glasses, which serve as a representative system for the MGFE in the literature, demonstrate that this approach succeeds to predict the behavior of the activation energy. In a further part of the thesis, Reverse Monte Carlo (RMC) simulations for the atomic structure of sodium borophosphate glasses are carried out with X-ray and neutron diffraction data as further input from experiments. Three-dimensional structures could be successfully generated that are in agreement with all experimental and theoretical constraints. Volume fractions of the ionic conduction pathways determined from these structures, however, do not show a substantial relationship to the activation energy, as earlier proposed in the iterature for alkali borate and alkali phosphate glasses.

The first part of the present Phd thesis is devoted to transport investigations in disordered quantum systems. We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially disordered and/or percolated quantum systems in the limit of high temperatures and low fillings using linear response theory. We find the transport behavior for some models to be in accord with a Boltzmann equation, i.e., long mean free paths, exponentially decaying currents although there are no band-structures to start from, while this does not apply to other models even though they are also almost completely delocalized. The second part of the present PhD thesis addresses the issue of initial state independence (ISI) in closed quantum system. The relevance of the eigenstate thermalization hypothesis (ETH) for the emergence of ISI equilibration is to some extent addressed. To this end, we investigate the Heisenberg spin-ladder and check the validity of the ETH for the energy difference operator by examining the scaling behavior of the corresponding ETH-fluctuations, which we compute using an innovative numerical method based on typicality related arguments. While, the ETH turns out to hold for the generic non-integrable models and may therefore serve as the key mechanism for ISI for this cases, it does not hold for the integrable Heisenberg-chain. However, close analysis on the dynamic of substantially out-of-equilibrium initial states indicates the occurrence of ISI equillibration in the thermodynamic limit regardless of whether the ETH is violated. Thus, we introduce a new parameter $v$, which we propose as an alternative of the ETH to indicate ISI equillibration in cases, in which the ETH does not strictly apply.

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