Model calculations on the influence of quantum electrodynamical effects on the chemistry of superheavy elements.

Using a phenomenological model, the influence of quantum electrodynamical effects on the prediction of the chemical behavior of superheavy elements within a relativistic Dirac-Slater calculation was investigated. This influence will be small and nondetectable for elements up to Z = 114. For elements near Z = 164 some changes in the ground state configurations occur but the chemical behavior will not change. Using this heuristic model, it is also possible to calculate elements beyond Z = 175. As an example we have chosen element E184 and are now able to make more valid speculations about the chemical behavior of the element than Penneman and co-workers could.

X-Ray spectra of superheavy and quasi-superheavy elements

We discuss the possibility of identifying superheavy elements from the observation of their M-shell x-ray spectra, which might occur during the collision of a superheavy element with a heavy target. The same question is discussed for the possible observation of the x-rays from the quasimolecule (quasi-superheavy element) which is formed during such a heavy-ion collision. It is shown that it is very difficult, if not impossible, to determine any information about the interesting quantum electrodynamical effects from the M-shell x-ray spectra of these quasimolecules.

Root effects on the turnover of grain legume residues in soil

Das Ziel dieser Arbeit war, die Einflüsse von Wurzeln und Rhizodeposition auf den Umsatz von Körnerleguminosenresiduen und damit verknüpfte mikrobielle Prozesse zu untersuchen. In einem integrierten Versuch wurden Ackerbohne (Vicia faba L.), Erbse (Pisum sativum L.) und Weiße Lupine (Lupinus albus L.) untersucht. Der Versuch bestand aus drei Teilen, zwei Gefäß-Experimenten und einem Inkubationsexperiment, in denen ausgehend von einem Gefäß-Experiment derselbe Boden und dasselbe Pflanzenmaterial verwendet wurden. In Experiment I wurde die Stickstoff-Rhizodeposition der Körnerleguminosenarten, definiert als wurzelbürtiger N nach dem Entfernen aller sichtbaren Wurzeln im Boden, gemessen und der Verbleib des Rhizodepositions-N in verschiednenen Bodenpools untersucht. Dazu wurden die Leguminosen in einem Gefäßversuch unter Verwendung einer in situ 15N-Docht-Methode mit einer 15N Harnstofflösung pulsmarkiert. In Experiment II wurde der Umsatz der N-Rhizodeposition der Körnerleguminosen und der Einfluss der Rhizodeposition auf den anschließenden C- und N-Umsatz der Körnerleguminosenresiduen in einem Inkubationsexperiment untersucht. In Experiment III wurde der N-Transfer aus den Körnerleguminosenresiduen einschließlich N-Rhizodeposition in die mikrobielle Biomasse und die Folgefrüchte Weizen (Triticum aestivum L.) und Raps (Brassica napus L.) in einem Gewächshaus-Gefäßversuch ermittelt. Die in situ 15N Docht-Markierungs-Methode wies hohe 15N Wiederfindungsraten von ungefähr 84 Prozent für alle drei Leguminosenarten auf und zeigte eine vergleichsweise homogene 15N Verteilung zwischen verschiedenen Pflanzenteilen zur Reife. Die Wurzeln zeigten deutliche Effekte auf die N-Dynamik nach dem Anbau von Körnerleguminosen. Die Effekte konnten auf die N-Rhizodeposition und deren anschließenden Umsatz, Einflüsse der Rhizodeposition von Körnerleguminosen auf den anschließenden Umsatz ihrer Residuen (Stängel, Blätter, erfassbare Wurzeln) und die Wirkungen nachfolgender Nichtleguminosen auf den Umsatzprozess der Residuen zurückgeführt werden: Die N-Rhizodeposition betrug zur Reife der Pflanzen bezogen auf die Gesamt-N- Aufnahme 13 Prozent bei Ackerbohne und Erbse und 16 Prozent bei Weißer Lupine. Bezogen auf den Residual N nach Ernte der Körner erhöhte sich der relative Anteil auf 35 - 44 Prozent. Die N-Rhizodeposition ist daher ein wesentlicher Pool für die N-Bilanz von Körnerleguminosen und trägt wesentlich zur Erklärung positiver Fruchtfolgeeffekte nach Körnerleguminosen bei. 7 - 21 Prozent des Rhizodepositions-N wurden als Feinwurzeln nach Nasssiebung (200 µm) wiedergefunden. Nur 14 - 18 Prozent des Rhizodepositions-N wurde in der mikrobiellen Biomasse und ein sehr kleiner Anteil von 3 - 7 Prozent in der mineralischen N Fraktion gefunden. 48 bis 72 Prozent der N-Rhizodeposition konnte in keinem der untersuchten Pools nachgewiesen werden. Dieser Teil dürfte als mikrobielle Residualmasse immobilisiert worden sein. Nach 168 Tagen Inkubation wurden 21 bis 27 Prozent des Rhizodepositions-N in den mineralisiert. Der mineralisierte N stammte im wesentlichen aus zwei Pools: Zwischen 30 Prozent und 55 Prozent wurde aus der mikrobiellen Residualmasse mineralisiert und eine kleinere Menge stammte aus der mikrobielle Biomasse. Der Einfluss der Rhizodeposition auf den Umsatz der Residuen war indifferent. Durch Rhizodeposition wurde die C Mineralisierung der Leguminosenresiduen nur in der Lupinenvariante erhöht, wobei der mikrobielle N und die Bildung von mikrobieller Residualmasse aus den Leguminosenresiduen in allen Varianten durch Rhizodepositionseinflüsse erhöht waren. Das Potential des residualen Körnerleguminosen-N für die N Ernährung von Folgefrüchten war gering. Nur 8 - 12 Prozent des residualen N wurden in den Folgenfrüchten Weizen und Raps wiedergefunden. Durch die Berücksichtigung des Rhizodepositions-N war der relative Anteil des Residual-N bezogen auf die Gesamt-N-Aufnahme der Folgefrucht hoch und betrug zwischen 18 und 46 Prozent. Dies lässt auf einen höheren N-Beitrag der Körnerleguminosen schließen als bisher angenommen wurde. Die residuale N-Aufnahme von Weizen von der Blüte bis zur Reife wurde durch den Residual-N gespeist, der zur Blüte in der mikrobiellen Biomasse immobilisiert worden war. Die gesamte Poolgröße, Residual-N in der mikrobiellen Biomasse und in Weizen, veränderte sich von der Blüte bis zur Reife nicht. Jedoch konnte ein Rest von 80 Prozent des Residual-N in keinem der untersuchten Pools nachgewiesen werden und dürfte als mikrobielle Residualmasse immobilisiert worden sein oder ist noch nicht abgebaut worden. Die zwei unterschiedlichen Folgefrüchte - Weizen und Raps - zeigten sehr ähnliche Muster bei der N-Aufnahme, der Residual-N Wiederfindung und bei mikrobiellen Parametern für die Residuen der drei Körnerleguminosenarten. Ein differenzierender Effekt auf den Umsatz der Residuen bzw. auf das Residual-N-Aneignungsvermögen der Folgefrüchte konnte nicht beobachtet werden.

High laser field effects in multiphoton ionization of Na_2

Femtosecond pump/probe multiphoton ionization experiments on Na_2 molecules are performed. The dependence of the total Na^+_2 ion signal on the delay time and the intensity of the femtosecond laser pulses is studied in detail. It is observed that molecular vibrational wavepacket motion in different electronic states dominates the time dependence of the ion signal. For higher laser intensities the relative contributions from the A ^1 \summe^+_u and the 2 ^1 \produkt__g states change dramatically, indicating the increasing importance of a two-electron versus a one-electron process. For even stronger fields (10 ^12 W/ cm²) a vibrational wavepacket in the electronic ground state X ^1 \summe^+_g is formed and its dynamics is also observed in the transient Na^+_2 signal. Time-dependent quantum calculations are presented. The theoretical results agree well with the experiment.

Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

Effects of tillage on processes of organic matter sequestration

To increase the organic matter (OM) content in the soil is one main goal in arable soil management. The adoption of tillage systems with reduced tillage depth and/or frequency (reduced tillage) or of no-tillage was found to increase the concentration of soil OM compared to conventional tillage (CT; ploughing to 20-30 cm). However, the underlying processes are not yet clear and are discussed contradictorily. So far, few investigations were conducted on tillage systems with a shallow tillage depth (minimum tillage = MT; maximum tillage depth of 10 cm). A better understanding of the interactions between MT implementation and changes in OM transformation in soils is essential in order to evaluate the possible contribution of MT to a sustainable management of arable soils. The objectives of the present thesis were (i) to compare OM concentrations, microbial biomass, water-stable aggregates, and particulate OM (POM) between CT and MT soils, (ii) to estimate the temporal variability of water-stable aggregate size classes occurring in the field and the dynamics of macroaggregate (>250 µm) formation and disruption under controlled conditions, (iii) to investigate whether a lower disruption or a higher formation rate accounts for a higher occurrence of macroaggregates under MT compared to CT, (iv) to determine which fraction is the major agent for storing the surplus of OM found under MT compared to CT, and (v) to observe the early OM transformation after residue incorporation in different tillage systems simulated. Two experimental sites (Garte-Süd and Hohes Feld) near Göttingen, Germany, were investigated. Soil type of both sites was a Haplic Luvisol. Since about 40 years, both sites receive MT by a rotary harrow (to 5-8 cm depth) and CT by a plough (to 25 cm depth). Surface soils (0-5 cm) and subsoils (10-20 cm) of two sampling dates (after fallow and directly after tillage) were investigated for concentrations of organic C (Corg) and total N (N), different water-stable aggregate size classes, different density fractions (for the sampling date after fallow only), microbial biomass, and for biochemically stabilized Corg and N (by acid hydrolysis; for the sampling date after tillage only). In addition, two laboratory incubations were performed under controlled conditions: Firstly, MT and CT soils were incubated (28 days at 22°C) as bulk soil and with destroyed macroaggregates in order to estimate the importance of macroaggregates for the physical protection of the very labile OM against mineralization. Secondly, in a microcosm experiment simulating MT and CT systems with soil <250 µm and with 15N and 13C labelled maize straw incorporated to different depths, the mineralization, the formation of new macroaggregates, and the partitioning of the recently added C and N were followed (28 days at 15°C). Forty years of MT regime led to higher concentrations of microbial biomass and of Corg and N compared to CT, especially in the surface soil. After fallow and directly after tillage, a higher proportion of water-stable macroaggregates rich in OM was found in the MT (36% and 66%, respectively) than in the CT (19% and 47%, respectively) surface soils of both sites (data shown are of the site Garte-Süd only). The subsoils followed the same trend. For the sampling date after fallow, no differences in the POM fractions were found but there was more OM associated to the mineral fraction detected in the MT soils. A large temporal variability was observed for the abundance of macroaggregates. In the field and in the microcosm simulations, macroaggregates were found to have a higher formation rate after the incorporation of residues under MT than under CT. Thus, the lower occurrence of macroaggregates in CT soils cannot be attributed to a higher disruption but to a lower formation rate. A higher rate of macroaggregate formation in MT soils may be due to (i) the higher concentrated input of residues in the surface soil and/or (ii) a higher abundance of fungal biomass in contrast to CT soils. Overall, as a location of storage of the surplus of OM detected under MT compared to CT, water-stable macroaggregates were found to play a key role. In the incubation experiment, macroaggregates were not found to protect the very labile OM against mineralization. Anyway, the surplus of OM detected after tillage in the MT soil was biochemically degradable. MT simulations in the microcosm experiment showed a lower specific respiration and a less efficient translocation of recently added residues than the CT simulations. Differences in the early processes of OM translocation between CT and MT simulations were attributed to a higher residue to soil ratio and to a higher proportion of fungal biomass in the MT simulations. Overall, MT was found to have several beneficial effects on the soil structure and on the storage of OM, especially in the surface soil. Furthermore, it was concluded that the high concentration of residues in the surface soil of MT may alter the processes of storage and decomposition of OM. In further investigations, especially analysis of the residue-soil-interface and of effects of the depth of residue incorporation should be emphasised. Moreover, further evidence is needed on differences in the microbial community between CT and MT soils.

Effects of different tillage treatments on labile soil organic matter pools and stabilization processes

An improved understanding of soil organic carbon (Corg) dynamics in interaction with the mechanisms of soil structure formation is important in terms of sustainable agriculture and reduction of environmental costs of agricultural ecosystems. However, information on physical and chemical processes influencing formation and stabilization of water stable aggregates in association with Corg sequestration is scarce. Long term soil experiments are important in evaluating open questions about management induced effects on soil Corg dynamics in interaction with soil structure formation. The objectives of the present thesis were: (i) to determine the long term impacts of different tillage treatments on the interaction between macro aggregation (>250 µm) and light fraction (LF) distribution and on C sequestration in plots differing in soil texture and climatic conditions. (ii) to determine the impact of different tillage treatments on temporal changes in the size distribution of water stable aggregates and on macro aggregate turnover. (iii) to evaluate the macro aggregate rebuilding in soils with varying initial Corg contents, organic matter (OM) amendments and clay contents in a short term incubation experiment. Soil samples were taken in 0-5 cm, 5-25 cm and 25-40 cm depth from up to four commercially used fields located in arable loess regions of eastern and southern Germany after 18-25 years of different tillage treatments with almost identical experimental setups per site. At each site, one large field with spatially homogenous soil properties was divided into three plots. One of the following three tillage treatments was carried in each plot: (i) Conventional tillage (CT) with annual mouldboard ploughing to 25-30 cm (ii) mulch tillage (MT) with a cultivator or disc harrow 10-15 cm deep, and (iii) no tillage (NT) with direct drilling. The crop rotation at each site consisted of sugar beet (Beta vulgaris L.) - winter wheat (Triticum aestivum L.) - winter wheat. Crop residues were left on the field and crop management was carried out following the regional standards of agricultural practice. To investigate the above mentioned research objectives, three experiments were conducted: Experiment (i) was performed with soils sampled from four sites in April 2010 (wheat stand). Experiment (ii) was conducted with soils sampled from three sites in April 2010, September 2011 (after harvest or sugar beet stand), November 2011 (after tillage) and April 2012 (bare soil or wheat stand). An incubation study (experiment (iii)) was performed with soil sampled from one site in April 2010. Based on the aforementioned research objectives and experiments the main findings were: (i) Consistent results were found between the four long term tillage fields, varying in texture and climatic conditions. Correlation analysis of the yields of macro aggregate against the yields of free LF ( ≤1.8 g cm-3) and occluded LF, respectively, suggested that the effective litter translocation in higher soil depths and higher litter input under CT and MT compensated in the long term the higher physical impact by tillage equipment than under NT. The Corg stocks (kg Corg m−2) in 522 kg soil, based on the equivalent soil mass approach (CT: 0–40 cm, MT: 0–38 cm, NT: 0–36 cm) increased in the order CT (5.2) = NT (5.2) < MT (5.7). Significantly (p ≤ 0.05) highest Corg stocks under MT were probably a result of high crop yields in combination with reduced physical tillage impact and effective litter incorporation, resulting in a Corg sequestration rate of 31 g C-2 m-2 yr-1. (ii) Significantly higher yields of macro aggregates (g kg-2 soil) under NT (732-777) and MT (680-726) than under CT (542-631) were generally restricted to the 0-5 cm sampling depth for all sampling dates. Temporal changes on aggregate size distribution were only small and no tillage induced net effect was detectable. Thus, we assume that the physical impact by tillage equipment was only small or the impact was compensated by a higher soil mixing and effective litter translocation into higher soil depths under CT, which probably resulted in a high re aggregation. (iii) The short term incubation study showed that macro aggregate yields (g kg-2 soil) were higher after 28 days in soils receiving OM (121.4-363.0) than in the control soils (22.0-52.0), accompanied by higher contents of microbial biomass carbon and ergosterol. Highest soil respiration rates after OM amendments within the first three days of incubation indicated that macro aggregate formation is a fast process. Most of the rebuilt macro aggregates were formed within the first seven days of incubation (42-75%). Nevertheless, it was ongoing throughout the entire 28 days of incubation, which was indicated by higher soil respiration rates at the end of the incubation period in OM amended soils than in the control soils. At the same time, decreasing carbon contents within macro aggregates over time indicated that newly occluded OM within the rebuilt macro aggregates served as Corg source for microbial biomass. The different clay contents played only minor role in macro aggregate formation under the particular conditions of the incubation study. Overall, no net changes on macro aggregation were identified in the short term. Furthermore, no indications for an effective Corg sequestration on the long term under NT in comparison to CT were found. The interaction of soil disturbance, litter distribution and the fast re aggregation suggested that a distinct steady state per tillage treatment in terms of soil aggregation was established. However, continuous application of MT with a combination of reduced physical tillage impact and effective litter incorporation may offer some potential in improving the soil structure and may therefore prevent incorporated LF from rapid decomposition and result in a higher C sequestration on the long term.

Effects of grassland conversion and tillage intensities on soil microbial biomass, residues and community structure

Agricultural intensification has a strong impact on level of soil organic matter (SOM), microbial biomass stocks and microbial community structure in agro-ecosystems. The size of the microbial necromass C pool could be about 40 times that of the living microbial biomass C pool in soils. Due to the specificity, amino sugar analysis gives more important information on the relative contribution of fungal and bacterial residues to C sequestration potential of soils. Meanwhile, the relationship between microbial biomass and microbial necromass in soil and its ecological significance on SOM are not fully understood and likely to be very complex in grassland soils. This thesis focuses on the effects of tillage, grassland conversion intensities and fertilisation on microbial biomass, residues and community structure. The combined analyses of microbial biomass and residue formation of both fungi and bacteria provided a unique opportunity to study the effect of tillage, grassland conversion and fertilisation on soil microbial dynamics. In top soil at 0-30 cm layer, a reduction in tillage intensity by the GRT and NT treatments increased the accumulation of saprotrophic fungi in comparison with the MBT treatment. In contrast, the GRT and NT treatments promoted AMF at the expense of saprotrophic fungi in the bottom soil layer at 30-40 cm depth. The negative relationship between the ergosterol to microbial biomass C ratio and the fungal C to bacterial C ratio points to the importance of the relationship between saprotrophic fungi and biotrophic AMF for tillage-induced changes in microbial turnover of SOC. One-season cultivation of winter wheat with two tillage events led to a significant loss in SOC and microbial biomass C stocks at 0-40 cm depth in comparison with the permanent grassland, even 5 years after the tillage event. However, the tillage induced loss in microbial biomass C was roughly 40% less in the long-term than in the short-term of the current experiment, indicating a recovery process during grassland restoration. In general, mould board tillage and grassland conversion to maize monoculture promoted saprotrophic fungi at the expense of biotrophic AMF and bacteria compared to undisturbed grassland soils. Slurry application promoted bacterial residues as indicated by the decreases in both, the ergosterol to microbial biomass C ratio and the fungal C to bacterial C ratio. In addition, the lost microbial functional diversity due to tillage and maize monoculture was restored by slurry application both in arable and grassland soils. I conclude that the microbial biomass C/S ratio can be used as an additional indicator for a shift in microbial community. The strong relationships between microbial biomass and necromass indices points to the importance of saprotrophic fungi and biotrophic AMF for agricultural management induced effects on microbial turnover and ecosystem C storage. Quantitative information on exact biomass estimates of these two important fungal groups in soil is inevitably necessary to understand their different roles in SOM dynamics.

Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.