The three Institutes of Physics of Universität Leipzig present their joint research report covering the year 2004. It documents the scientific progress made in various fields. The year has brought intensified collaboration within and between the Physics Institutes and with the outside world.

We welcome you to read about the progress of research at the three Institutes of Physics of Universität Leipzig in our joint report covering 2005.

In the following report we present our internal structure and document our scientific progress, sorted by the work groups. Many challenging scientific questions are worked on jointly by several groups, in cooperation with the local research institutes of Max-Planck-Gesellschaft and Leibniz-Gemeinschaft and of course with many colleagues worldwide. In the brief reports also the various sources of external funding, vital to our success, are gratefully acknowledged.

The year 2007 has been rich with events in our Physics Institutes, both scientific and social. In the short notes of this booklet we have compiled the most interesting results of our research, often performed in cooperation within and among the Physics Institutes and with many colleagues in Leipzig, nationally and worldwide.

In front of you is the 2008 report of the Physics Institutes of the Universität Leipzig. The year has brought a strong expansion of our interdisciplinary education and cooperation with chemistry and biochemistry in the framework of the Leipzig Graduate School of Natural Sciences "Building with Molecules and Nano-objects (BuildMoNa)", now hosting almost one hundred doctoral candidates. We particulary acknowledge the strong participation of our industrial partners in the teaching modules. The Graduate School is supported by the State of Saxony with two additional Research Units ("Nachwuchsforschergruppen") funded via ESF and having started in the meanwhile.

This 2009 report of the Physics Institutes of the Universität Leipzig presents to you an overview of our research in numerous projects, enjoyably conducted with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within the work groups.

This 2010 report of the Physics Institutes of the Universität Leipzig presents to you an overview of our research in numerous projects, enjoyably conducted with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within the work groups.

Welcome to the 2012 report of the Physics Institutes of the Universität Leipzig presenting to you an overview of our research in numerous projects. We have enjoyed research and interaction with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within the work groups.

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The pulsed gradient spin-echo nuclear magnetic resonance experiment is a powerful tool for studying the constitution and structure of complex systems (e.g., polydisperse systems and porous media). In applications to polydisperse systems, it is important to consider the effects of obstruction, exchange, entanglement, and diffusional averaging processes whereas in applications to porous samples, reliable structural information can only be extracted from the time-dependence of the apparent diffusion coefficient when the deleterious effects of spatially and/or temporally inhomogeneous background (magnetic field) gradients can be suppressed. These issues are considered in this review.