We present a novel approach to the investigation of transport coefficients in condensed matter systems, which is based on a pertinent time-convolutionless (TCL) projection operator technique. In this context we analyze in advance the convergence of the corresponding perturbation expansion and the influence of the occurring inhomogeneity. The TCL method is used to establish a formalism for a consistent derivation of a Boltzmann equation from the underlying quantum dynamics, which is meant to apply to non-ideal quantum gases. We obtain a linear(ized) collision term that results as a finite non-singular rate matrix and is thus adequate for further considerations, e.g., the calculation of transport coefficients. In the work at hand we apply the provided scheme to numerically compute the diffusion coefficient of an atomic wire and especially analyze its dependence on certain model properties, in particular on the width of the wire.

Quasi-particles formed in lithium niobate after pulse exposure were investigated by transient absorption and photoluminescence spectroscopy as well as numerical simulations. This includes the formation process, the transport through the crystal, interim pinning on defects during the relaxation process, and the final recombination with deep centers. It was shown that the charge-transport through the crystal can be described by a hopping transport including different types of hops between regular or defective lattice sites, i.e., the transport includes a mixture of free and bound small polarons. Furthermore, the different types of hops connected with varying activation energies and their distribution are responsible for an altered temporal decay curve when changing the crystal composition or temperature. Additionally, it was shown that the hitherto accepted recombination model is insufficient to describe all transient absorption and luminescence effects in lithium niobate under certain experimental conditions, i.e., long-living absorption dynamics in the blue/UV spectral range do not follow the typical polaron dynamics and cannot be described under the assumption of charge compensation. However, similar decay characteristics between self-trapped excitons known from photoluminescence spectroscopy and the unexpected behavior of the transient absorption were found leading to a revised model. This includes, besides the known polaron relaxation and recombination branch, a significant role of self-trapped excitons and their pinning on defects (pinned STEs). Since the consideration of further absorption centers in the relaxation path after pulse exposure might result in misinterpretations of previously determined polaron absorption cross-sections and shapes, the necessity to perform a review became apparent. Therefore, a supercontinuum pump-probe experiment was designed and all measurements applied under the same experimental conditions (temperature, polarization) so that one can extract the absorption amplitudes of the single quasi-particles in a spectral range of 0.7-3.0eV. The detailed knowledge might be used to deconvolve the absorption spectra and transform them to number densities of the involved centers which enables one to obtain an easier insight into recombination and decay dynamics of small polarons and self-trapped excitons. As the hopping transport of quasi-particles and the concept of pinned STEs might be fundamental processes, a thorough understanding opens up the possibility of their exploitation in various materials. In particular, results presented herein are not only limited to lithium niobate and its applications; an extension to a wide range of further strongly polar crystals in both their microscopic processes and their use in industry can be considered.

The present work broaches the physics of light-matter interaction, chiefly using nonlinear optical spectroscopy in a newly developed framework termed as Photon Management Concept. This way, existing fragments dealing with specific properties of harmonic and upconversion nanoparticles (HNPs/UCNPs) are consolidated into a full and coherent picture with the primary goal of understanding the underlying physical processes and their impact on the application side, especially in terms of imaging techniques, via suitable experimental and numerical studies. Contemporary optical setups involving contrast-enhancing agents are frequently limited in their excitation and detection configurations owing to a specialization to a select number of markers. As a result, the bandwidth of experimental methods and specimens that may be investigated is severely restricted in a large number of state-of-the-art setups. Here, an alternative approach involving HNPs and UCNPs, respectively, is presented providing an overview from their synthesis to optical characterization and to potential fields of application. Based on their inherent flexibility based on their nonlinear optical response, especially in terms of wavelength and intensity tunability, the PMC alleviates prevalent limitations by dynamically adapting the setup to a sample instead of the preliminary culling to a reduced number of eligible specimens that must not change their optical properties significantly during investigation. The use of HNPs supersedes such concerns due to their nearly instantaneously generated, strongly anti-Stokes shifted, coherent emission capable of producing radiation throughout the visible spectral range, including infrared and ultraviolet wavelengths. This way, HNPs transcend the traditional field of imaging and introduces potential applications in optomanipulation or holographic techniques. Thorough (nonlinear) optical characterization of UCNPs and alkali niobate HNP ensembles is performed to assess the fundamental physical mechanisms interwoven with numerical studies leading to their wide-ranging applicability. Final remarks show that HNPs are ideal candidates for realization of the PMC and yet hold an even further potential beyond current prospects.