Magnetic fields influence the rate and/or yield of chemical reactions that proceed via spin correlated radical pair intermediates. The field of spin chemistry centres around the study of such magnetic field effects (MFEs). This thesis is particularly concerned with the effects of the weak magnetic fields B₀ ~ 1mT relevant in the ongoing debates on the mechanism by which animals sense the geomagnetic field and on the putative health effects of environmental electromagnetic fields. Relatively few previous studies have dealt with such weak magnetic fields. This thesis presents several new theoretical tools and applies them to interpret experimental measurements. Chapter 1 surveys the development and theory of spin chemistry. Chapter 2 introduces the use of Tikhonov and Maximum Entropy Regularisation methods as a new means of analysing MARY field effect data. These are applied to recover details of the diffusive motion of reacting pyrene and N,N-dimethylaniline radicals. Chapter 3 gives a fresh derivation and appraisal of an approximate, semiclassical approach to MFEs. Monte Carlo calculations allow the elucidation of several "rules of thumb" for interpreting MFE data. Chapter 4 discusses recent optically-detected zero-field EPR measurements, adapting the gamma-COMPUTE algorithm from solid state NMR for their interpretation. Chapter 5 explores the role of RF polarisation in producing MFEs. The breakdown in weak fields of the familiar rotating frame approximation is analysed. Chapter 6 reviews current knowledge and landmark experiments in the area of animal magnetoreception. The origins of the sensitivity of European robins Erithacus rubecula to the Earth’s magnetic field are given particular attention. In Chapter 7, Schulten and Ritz’s hypothesis that avian magnetoreception is founded on a radical pair mechanism (RPM) reaction is appraised through calculations in model systems. Chapter 8 introduces quantitative methods of analysing anisotropic magnetic field effects using spherical harmonics. Chapter 9 considers recent observations that European robins may sometimes be disoriented by minuscule RF fields. These are shown to be consistent with magnetoreception via a radical pair with no (effective) magnetic nuclei in one of the radicals.

The work at hand presents a novel approach to transport in closed quantum systems. To this end a method is introduced which is essentially based on projection operator techniques, in particular on the time-convolutionless (TCL) technique. The projection onto local densities of quantities such as energy, magnetization, particles, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. Especially, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems. The term modular basically corresponds to (quasi-) one-dimensional structures consisting of identical or at least similar many-level subunits. Modular quantum systems are demonstrated to represent many physical situations and several examples are given. In the context of these quantum systems lowest order TCL is shown as an efficient tool which also allows to investigate the dependence of transport on the considered length scale. In addition an estimation for the validity range of lowest order TCL is derived. As a first application a "design" model is considered for which a complete characterization of all available transport types as well as the transitions to each other is possible. For this model the relationship to quantum chaos and the validity of the Kubo formula is further discussed. As an example for a "real" system the Anderson model is finally analyzed. The results are partially verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization or approximative integrators.