This work presents an overview of several different methods for construct- ing ultrafilters. The first part contains constructions not needing additional assumptions beyond the usual axioms of Set Theory. K. Kunen's method using independent systems for constructing weak P-points is presented. This is followed by a presentation of its application in topology (the proof of the existence of sixteen topological types due to J. van Mill). Finally a new con- struction due to the author is presented together with a proof of his result, the existence of a seventeenth topological type: ω∗ contains a point which is discretely untouchable, is a limit point of a countable set and the countable sets having it as its limit point form a filter. The second part looks at constructions which use additional combina- torial axioms and/or forcing. J. Ketonen's construction of a P-point and A. R. D. Mathias's construction of a Q-point are presented in the first two sections. The next sections concentrate on strong P-points introduced by C. Laflamme. The first of these contains a proof of a new characterization theorem due jointly to the author, A. Blass and M. Hrušák: An ultrafilter is Canjar if and only if it is a strong P-point. A new proof of Canjar's the- orem on the existence of non-dominating filters (Canjar filters) which uses...

Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.

This thesis deals with the influence of TV series and their strong heroines on female audience. The aim of this work is to find out whether selected female characters influence the general view of the femine beauty ideal, whether the viewers were in any way inspired by strong female characters and whether these series have opened up some social issues. These goals were formulated into three research questions, which will be answered in the conclusion. The work is divided into three main parts - theoretical, methodological and practical. The theoretical part aims to acquaint the reader with the theoretic basis needed to understand the researched issues. The methodological part presents research methods with all its advantages and disadvantages. The last practical part is focused on research and interpretation of the obtained data. A qualitative method is used to achieve the results, specifically the grounded theory, which is used for the analysis and subsequent interpretation of data obtained from interviews.

The goal of the original research presented in this thesis is to study the strong coupling regime of Quantum Field Theories (QFTs) with different methods, making concrete predictions about the phase structure and the dynamics of these theories, and on their observables. The focus is on (gauge) field theories in three spacetime dimensions, which are an interesting laboratory to understand the properties of strong coupling in setups that are usually simpler than in the more familiar case of gauge theories in four dimensions. Importantly, topological effects play a relevant role in three dimensions, thanks to the presence of the so-called Chern-Simons term.The thesis contains a short introduction to QFTs in 3d, principles and applications of infrared dualities, large N techniques, and holography. Indeed, the web of infrared dualities, the large N expansion, and the holographic correspondence between QFT and gravity are the main tools which we use to investigate the strongly coupled regimes of 3d QFTs.Then, the original material is presented. In a first line of research, we focus on the study of the phase diagram of a 3d gauge theory making use of conjectured infrared dualities, extending such dualities to the case where more than one mass parameter can be dialed. In a second line of research, we study a class of 3d gauge theories by engineering their gravity dual in a string theory setup. We prove the existence of multiple phase transitions between phases characterized by both massless particles and topological sectors. In a third line of research, we use holography as a tool to explore the interplay between the physics of 4d QCD and 3d gauge theories. In particular, we analyze the properties of 3d domain walls, which appear as soliton-like solutions of 4d QCD in specific parametric regimes. Finally, we propose a boundary construction of 3d large N vector models, which appear as critical points of theories obtained by coupling degrees of freedom localized on a 3d boundary to a 4d bulk theory. This construction allows to prove new dualities and uncovers a new computational tool for 3d vector models. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

<p>This dissertation establishes limit theory for topological functionals of geometric complexes from a stochastic process viewpoint. Standard filtrations of geometric complexes, such as the Čech and Vietoris-Rips complexes, have a natural parameter <i>r </i>which governs the formation of simplices: this is the basis for persistent homology. However, the parameter <i>r</i> may also be considered the time parameter of an appropriate stochastic process which summarizes the evolution of the filtration.</p><p>Here we examine the stochastic behavior of two of the foremost classes of topological functionals of such filtrations: the Betti numbers and the Euler characteristic. There are also two distinct setups in which the points underlying the complexes are generated, where the points are distributed randomly in <i>R^d</i> according to a general density (the traditional setup) and where the points lie in the tail of a heavy-tailed or exponentially-decaying “noise” distribution (the extreme-value theory (EVT) setup).<br></p><p>These results constitute some of the first results combining topological data analysis (TDA) and stochastic process theory. The first collection of results establishes stochastic process limits for Betti numbers of Čech complexes of Poisson and binomial point processes for two specific regimes in the traditional setup: the sparse regime—when the parameter <i>r </i>governing the formation of simplices causes the Betti numbers to concentrate on components of the lowest order; and the critical regime—when the parameter <i>r</i> is of the order <i>n^-1/d</i> and the geometric complex becomes highly connected with topological holes of every dimension. The second collection of results establishes a functional strong law of large numbers and a functional central limit theorem for the Euler characteristic of a random geometric complex for the critical regime in the traditional setup. The final collection of results establishes functional strong laws of large numbers for geometric complexes in the EVT setup for the two classes of “noise” densities mentioned above.<br></p>

The central problem in the modern electronic structure theory is the calculation of cor- relation energy, possibly by an approach that would account for both static and dynamic correlation in an efficient, balanced and accurate way. In this thesis, I present a collection of methods that combine the effective treatment of dynamic correlation by the coupled cluster theory with density matrix renormalization group, a well-established technique for calculations of strongly correlated systems. The connection between them is achieved via the tailored coupled clusters (TCC) ansatz, which conveniently does not impose any ad- ditional computational costs. After the successful initial assessment, we developed more efficient implementations of these methods by employing the local approaches based on pair natural orbitals. This way, we extended the range of possible applications to larger systems with thousands of basis functions. To assess the accuracy of TCC as well as its local counterparts, we performed a variety of benchmark calculations ranging from small, yet challenging systems such as the nitrogen molecule or tetramethyleneethane diradical, to larger molecules like oxo-Mn(Salen) or Fe(II)-porphyrin model. 1

Asymmetric Conflicts from 1989 - 2001 in quantitative analysis Abstract Following paper discuses two significant concepts in the area of asymmetric warfare. Both are dealing with the phenomenon of weak actors winning in armed conflicts. Ivan Arreguín-Toft is discussing the role of strategic asymmetry and concludes that the strategy actors choose is directly influencing the result of the conflict. Andrew Mack is dealing with the interest asymmetry, saying that strong actors tend to lose because their interest to win is usually weaker than that of their small opponents. In the same time strong actors are politically more vulnerable based on the level of democracy. Both theories are tested by quantitative analysis of all asymmetric conflicts that took place between 1989 and 2000. Values related to strategies, results, strength of the actors, interest and level of democracy are assigned to all conflicts based on information provided in conflict and other databases.

Philosophiae Doctor - PhD / In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1,2. In the binary case, results are extended to codes from neighbourhood designs of the line graphs Li+l(Kn) using certain elementary relations. Codes from incidence designs of complete graphs, Kn' and neighbourhood designs of their line graphs, £1(Kn) (the so-called triangular graphs), have been considered elsewhere by others. We consider codes from incidence designs of Ll(Kn) and L2(Kn), and neighbourhood designs of L2(Kn) and L3(Kn). In each case, the basic parameters of the codes are determined. Further, we introduce a family of vertex-transitive graphs Rn that are embeddable into the strong product Ll(Kn) ~ K2' of triangular graphs and K2' a class that at first sight may seem unnatural but, on closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, Rn also has what we have termed as 6-cycle designs. These are designs in which the point set contains vertices of the graph and every block contains vertices of a 6-cycle in the graph. Also, binary codes from incidence matrices of these graphs have other minimum words in addition to incidence vectors of the blocks. In addition, these graphs have induced subgraphs isomorphic to the family Hn of complete porcupines (see Definition 4.11). We describe codes from incidence matrices of Rn and Hn and determine their parameters. The discussion is concluded with a look at complements of Rn and Hn, respectively denoted by Rn and Hn. Among others, the complements rn are contained in the union of the categorical product Ll(Kn) x Kn' and the categorical product £1(Kn) x Kn (where £1(Kn) is the complement of the iii triangular graph £1(Kn)). As with the other graphs, we have also considered codes from the span of incidence matrices of Rn and Hn and determined some of their properties. In each case, automorphisms of the graphs, designs and codes have been determined. For the codes from incidence designs of triangular graphs, embeddings of Ll(Kn) x K2 and complements of complete porcupines, we have exhibited permutation decoding sets (PD-sets) for correcting up to terrors where t is the full error-correcting capacity of the codes. For the remaining codes, we have only been able to determine PD-sets for which it is possible to correct a fraction of t-errors (partial permutation decoding). For these codes, we have also determined the number of errors that can be corrected by permutation decoding in the worst-case.

<p>The strong metal support interaction (SMSI) is among the best-known classes of metal-oxide interfacial interactions in heterogeneous catalysis, which is defined by the coverage of surface oxide on metal nanoparticles, forming a metal-oxide interface. However, there is limited insight in the atomic scale understanding of the structure of the SMSI oxide. In this work, surface science techniques including scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), high-resolution electron energy loss spectroscopy (HREELS) and low energy electron diffraction (LEED) were employed to investigate interfacial interactions in multiple catalytic systems, including ZnO-Pd, ZnO-Pt, and MoOx-Pt. To utilize the capabilities of the surface science techniques and to mimic a catalytic metal nanoparticle in SMSI state, ultrathin oxide films were prepared on metal single crystals as inverse model catalysts.</p> <p>The structural and chemical transformations of ultrathin zinc (hydroxy)oxide films on Pd(111) were studied under varying gas phase conditions (UHV, 5×10−7 mbar of O2 and D2/O2 mixture). Under oxidative conditions, zinc oxide forms partially hydroxylated bilayer islands on Pd(111). Sequential treatments of the submonolayer ZnOxHy films in D2/O2 mixture (1:4) at 550 K evoked structural transformations from bilayer to monolayer and to a PdZn near-surface alloy, in accompany with the reduction of Zn, demonstrating that zinc oxide as a non-reducible oxide, can spread on metal surface and show an SMSI-like behavior in the presence of hydrogen. A mixed canonical – grand canonical phase diagram revealed that the monolayer intermediate structure is a metastable structure formed during the kinetic transformation, and the near-surface alloys are stable under the D2/O2 conditions. Grand canonical phase diagram predicted that under real SMSI conditions zinc oxide films on Pd nanoparticles would be stabilized by hydroxylation with stoichiometries such as ZnOH and Zn2O3H3. Based on the experimental and theoretical observations, we propose that the mechanism of metal nanoparticle encapsulation involves both surface (hydroxy)oxide formation as well as alloy formation, depending on the environmental conditions.</p> <p>Hydroxylation plays a more important role in the ZnO/Pt(111) system. Different from Pd(111), zinc oxide tends to form monolayer graphite-like ZnO films on Pt(111) under oxidative conditions at submonolayer coverages. This structure is extremely susceptible to hydroxylation at room temperature, leading to spontaneous formation of honeycomb-like Zn6O5H5 films in hydrogen. The interaction of the two distinct structures with Pt were investigated by XPS, STM, and HREELS with CO, C2H4, and NO as probe molecules. Zn exhibits a partially reduced oxidation state in Zn6O5H5 and donates negative charge to surface Pt in the confined rings, leading to a switch from linear CO adsorption to bridged CO adsorption in accompany with a 50 cm-1 shift of ν(CO) towards lower frequencies. C2H4 readily forms ethylidyne (*CCH3) species at room temperature once adsorbed on Pt(111), while the formation of ethylidyne is weakened on the Zn6O5H5/Pt(111) surface. In summary, this study demonstrated a unique metal-hydroxide interaction, which serves as a novel approach for the modification of metal catalysts.</p> <p>The partial coverage of metal surfaces by oxides could be utilized to passivate specific sites of catalysts, improving the activity and stability. Herein, we studied the structure of surface Mo oxides on Pt(111) and Pt(544) using STM, XPS, and HREELS. At 0.08 ML coverage, Mo oxide tends to form 1~2 nm clusters and the majority of Mo is in +5 oxidation state. The Mo oxide clusters tend to aggregate near the monoatomic Pt steps, showing a higher local density compared to the wide terraces. Therefore, our results provide experimental evidence for the site-selective growth of Mo oxides at step sites, which could prevent the leaching of active component in catalysts under real reaction conditions.</p> <p>Overall, through atomic-level characterization of inverse model catalysts, we provided insights into the nature of metal-oxide interactions in multiple systems. The surface oxide films influence the property of metal surfaces in various ways, including migration, alloy formation, electronic perturbation, geometric confinement, and site-selective blocking. These findings emphasize the necessity of understanding the real structure of catalytic surfaces under different reaction conditions and shed light on rational design of oxide supported metal nanoparticle catalysts.</p>

When calculating the dynamics of a quantum system, including the effect of its environment is highly relevant since virtually any real quantum system is exposed to environmental influences. It has turned out that the widely used perturbative approaches to treat such so-called open quantum systems have severe limitations. Furthermore, due to current experiments which have implemented strong system-environment interactions the non-perturbative regime is far from being academical. Therefore determining the exact dynamics of an open quantum system is of fundamental relevance. The hierarchy of pure states (HOPS) formalism poses such an exact approach. Its novel and detailed derivation, as well as several numerical aspects constitute the main methodical part of this work. Motivated by fundamental issues but also due to practical relevance for real world devices exploiting quantum effects, the entanglement dynamics of two qubits in contact with a common environment is investigated extensively. The HOPS formalism is based on the exact stochastic description of open quantum system dynamics in terms of the non-Markovian quantum state diffusion (NMQSD) theory. The distinguishing and numerically beneficial features of the HOPS approach are the stochastic nature, the implicit treatment of the environmental dynamics and, related to this, the enhanced statistical convergence (importance sampling), as well as the fact that only pure states have to be propagated. In order to claim that the HOPS approach is exact, we develop schemes to ensure that the numerical errors can be made arbitrarily small. This includes the sampling of Gaussian stochastic processes, the multi-exponential representation of the bath correlation function and the truncation of the hierarchy. Moreover, we incorporated thermal effects on the reduced dynamics by a stochastic Hermitian contribution to the system Hamiltonian. In particular, for strong system-environment couplings this is very beneficial for the HOPS. To confirm the accuracy assertion we utilize the seemingly simple, however, non-trivial spin-boson model to show agreement between the HOPS and other methods. The comparison shows the HOPS method’s versatile applicability over a broad range of model parameters including weak and strong coupling to the environment, as well as zero and high temperatures. With the gained knowledge that the HOPS method is versatile and accurately applicable, we investigate the specific case of two qubits while focusing on their entanglement dynamics. It is well known that entanglement, the relevant property when exploiting quantum effects in fields like quantum computation, communication and metrology, is fragile when exposed to environmental noise. On the other hand, a common environment can also mediate an effective interaction between the two parties featuring entanglement generation. In this work we elucidate the interplay between these competing effects, focusing on several different aspects. For the perturbative (weak coupling) regime we enlighten the difficulties inherent to the frequently used rotating wave approximation (RWA), an approximation often applied to ensure positivity of the reduced state for all times. We show that these difficulties are best overcome when simply omitting the RWA. The seemingly unphysical dynamics can still be used to approximate the exact entanglement dynamics very well. Furthermore, the influence of the renormalizing counter term is investigated. It is expected that under certain conditions (adiabatic regime) the generation of entanglement is suppressed by the presence of the counter term. It is shown, however, that for a deep sub-Ohmic environment this expectation fails. Leaving the weak coupling regime, we show that the generation of entanglement due to the influence of the common environment is a general property of the open two-spin system. Even for non-zero temperatures it is demonstrated that entanglement can still be generated and may last for arbitrary long times. Finally, we determine the maximum of the steady state entanglement as a function of the coupling strength and show how the known delocalization-to-localization phase transition is reflected in the long time entanglement dynamics. All these results require an exact treatment of the open quantum system dynamics and, thus, contribute to the fundamental understanding of the entanglement dynamics of open quantum systems. / Bei der Bestimmung der Dynamik eines Quantensystems ist die Berücksichtigung seiner Umgebung von großem Interessen, da faktisch jedes reale Quantensystem von seiner Umgebung beeinflusst wird. Es zeigt sich, dass die viel verwendeten störungstheoretischen Ansätze starken Einschränkungen unterliegen. Außerdem, da es in aktuellen Experimenten gelungen ist starke Wechselwirkung zwischen dem System und seiner Umgebung zu realisieren, gewinnt das nicht-störungstheoretischen Regime stets an Relevanz. Dementsprechend ist die Berechnung der exakten Dynamik offener Quantensysteme von grundlegender Bedeutung. Einen solchen exakten nummerischen Zugang stellt der hierarchy of pure states (HOPS) Formalismus dar. Dessen neuartige und detaillierte Herleitung, sowie diverse nummerische Aspekte werden im methodischen Teil dieser Arbeit dargelegt. In vielerlei Hinsicht relevant folgt als Anwendung eine umfangreiche Untersuchung der Verschränkungsdynamik zweier Qubits unter dem Einfluss einer gemeinsamen Umgebung. Vor allem im Hinblick auf die experimentell realisierbare starke Kopplung mit der Umgebung ist dieses Analyse von Interesse. Der HOPS Formalismus basiert auf der stochastischen Beschreibung der Dynamik offener Quantensysteme im Rahmen der non-Markovian quantum state diffusion (NMQSD) Theorie. Der stochastische Charakter der Methode, die implizite Berücksichtigung der Umgebungsdynamik, sowie das damit verbundene Importance Sampling, als auch die Tatsache dass lediglich reine Zustände propagiert werden müssen unterscheidet diese Methode maßgeblich von anderen Ansätzen und birgt numerische Vorteile. Um zu behaupten, dass die HOPS Methode exakte Ergebnisse liefert, müssen auftretenden nummerischen Fehler beliebig klein gemacht werden können. Ein grundlegender Teil der hier vorgestellten methodischen Arbeit liegt in der Entwicklung diverser Schemata, die genau das erreichen. Dazu zählen die numerische Realisierung von Gauss’schen stochastischen Prozessen, die Darstellung der Badkorrelationsfunktion als Summe von Exponentialfunktionen sowie das Abschneiden der Hierarchie. Außerdem wird gezeigt, dass sich der temperaturabhängige Einfluss der Umgebung durch einen stochastischen Hermiteschen Beitrag zum System-Hamiltonoperator berücksichtigen lässt. Vor allem bei starker Kopplung ist diese Variante besonders geeignet für den HOPS Zugang. Um die Genauigkeitsbehauptung der HOPS Methode zu überprüfen wird die Übereinstimmung mit anderen Methode gezeigt, wobei das vermeintlich einfachste, jedoch nicht triviale spin-boson-Modell als Testsystem verwendet wird. Diese Untersuchung belegt, dass die HOPS Methode für eine Vielzahl an Szenarien geeignet ist. Das beinhaltet schwache und starke Kopplung an die Umgebung, sowie Temperatur null als auch hohe Temperaturen. Mit dem gewonnenen Wissen, dass die HOPS Methode vielseitig einsetzbar ist und genaue Ergebnisse liefert wird anschließend der spezielle Fall zweier Qubits untersucht. Im Hinblick auf die Ausnutzung von Quanteneffekten in Bereichen wie Rechentechnik, Kommunikation oder Messtechnik liegt der primäre Fokus auf der Dynamik der Verschränkung zwischen den Qubits. Es ist bekannt, dass durch von außen induziertes Rauschen die Verschränkung im Laufe der Zeit abnimmt. Andererseits weiß man auch, dass eine gemeinsame Umgebung zu einer effektiven Wechselwirkung zwischen den Qubits führt, welche Verschränkung aufbauen kann. In dieser Arbeit wird das Wechselspiel zwischen diesen beiden gegensätzlichen Effekten untersucht, wobei die folgenden Aspekte beleuchtet werden. Für den Fall schwacher Kopplung, wo eine störungstheoretische Behandlung in Frage kommt, werden die Probleme der rotating wave approximation (RWA) analysiert. Diese Näherung wird häufig verwendet um die Positivität des reduzierten Zustands zu allen Zeiten zu gewährleisten. Es wird gezeigt, dass sich diese Probleme am besten vermeiden lassen, wenn die RWA einfach weggelassen wird. Die auf den ersten Blick nicht-physikalische Dynamik ist sehr gut geeignet um die exakte Verschränkungsdynamik näherungsweise wiederzugeben. Des Weiteren wird der Einfluss der Renormalisierung des sogenannten counter terms untersucht. Unter bestimmten Voraussetzungen (adiabatisches Regime) ist zu erwarten, dass der Verschränkungsaufbau durch den counter term verhindert wird. Es zeigt sich, dass für eine sehr sub-Ohm’sche Umgebung (deep sub-Ohmic regime) diese Erwartung nicht zutrifft. Weiterhin wird der Fall starker Kopplung zwischen dem zwei-Qubit-System und der Umgebung betrachtet. Die Berechnungen zeigen das generelle Bild, dass sich zwei nicht wechselwirkende Qubits durch den Einfluss einer gemeinsamen Umgebung verschränken. Selbst bei Temperaturen größer als null kann Verschränkung aufgebaut werden und auch für beliebig lange Zeiten erhalten bleiben. In einem letzten Punkt wird das Maximum der stationären Verschränkung (Langzeit-Limes) in Abhängigkeit von der Kopplungsstärke bestimmt. Dabei wird gezeigt, dass sich der bekannte Phasenübergang von Delokalisierzung zu Lokalisierung auch in der Langzeitdynamik der Verschränkung widerspiegelt. All diese Erkenntnisse erfordern eine exakte Behandlung der offenen Systemdynamik und erweitern somit das fundamentalen Verständnis der Verschränkungsdynamik offener Quantensysteme.