Motivated by the sustained interest in Bose Einstein condensates and the recent progress in the understanding of topological phases in condensed matter systems, we study quantum condensates and possible topological phases of bosons in coupled light-matter excitations, so-called polaritons. These bosonic quasi-particles emerge if electronic excitations (excitons) couple strongly to photons. In the first part of this thesis a polariton Bose Einstein condensate in the presence of disorder is investigated. In contrast to the constituents of a conventional condensate, such as cold atoms, polaritons have a finite life time. Then, the losses have to be compensated by continued pumping, and a non-thermal steady state can build up. We discuss how static disorder affects this non-equilibrium condensate, and analyze the stability of the superfluid state against disorder. We find that disorder destroys the quasi-long range order of the condensate wave function, and that the polariton condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. Furthermore, we analyze the far field emission pattern of a polariton condensate in a disorder environment in order to compare directly with experiments. In the second part of this thesis features of polaritons in a two-dimensional quantum spin Hall cavity with time reversal symmetry are discussed. We propose a topological invariant which has a nontrivial value if the quantum spin Hall insulator is topologically nontrivial. Furthermore, we analyze emerging polaritonic edge states, discuss their relation to the underlying electronic structure, and develop an effective edge state model for polaritons.

Diese Arbeit beschreibt die Suche nach dem Higgs Boson, welches in vielen theoretischen Modellen der Teilchenphysik vorhergesagt wird. Das Higgs Boson ist die Konsequenz der spontanen Symmetriebrechung, welche den Teilchen Masse verleiht. Zur Suche werden e+e- Annihilationen bei Schwerpunktenergien bis 209 GeV analysiert, welche vom Experiment L3 am Speicherring LEP in den Jahren 1998 bis 2000 registriert wurden. Die Suche erfolgte in allen relevanten Endzustaenden, wobei der Endzustand mit vier hadronischen Jets im Detail behandelt wird. Die Daten werden mit den Erwartungen eines Signals in verschiedenen Modellen bei Beruecksichtigung der bekannten Untergrundprozesse verglichen oder es wird modellunabhaengig nach der Erzeugung skalarer Teilchen gesucht. Die Produktion von Higgs Bosonen konnte nicht nachgewiesen werde. Die Daten wurden daher benutzt, um neue Grenzen fuer Parameter der Modelle oder der Kopplungen zu setzen. Als erstes wird die Suche nach dem Higgs Boson im Standard Modell der elektroschwachen Wechselwirkung beschrieben. Die Produktion des Higgs Bosons wird bei LEP Energien ueber die Higgs-Strahlung und der Zerfall des Higgs Bosons in ein Paar von b-Quarks vorhergesagt. Die Analysen beruhen daher wesentlich auf der Erkennung von B-Hadronen. Der HZ->qqqq Endzustand wird im Detail untersucht, und die Ergebnisse werden mit den anderen Kanaelen : HZ->qqvv, HZ->qql+l- und HZ->tau+tau- qq kombiniert. Die untere Massengrenze fuer das Higgs Boson wird zu mH > 112.0 GeV auf 95% Vertrauensniveau, bestimmt. Ausserdem werden Grenzen auf die HZZ Kopplung abgeleitet. Im minimalen supersymmetrischen Modell (MSSM) werden fuenf Higgs Bosonen vorhergesagt. Zur Higgs-Strahlung kommt die Paarproduktion von Higgs Bosonen, e+e- -> hA , hinzu. Die Ergebnisse der Suche im Standard Modell werden durch die Suche in den Endzustaenden bb tau+tau- (tau+tau- bb), bbbb und hZ->AAqq ergaenzt. Im Rahmen von drei Standard-Szenarien, benannt als "mh-max", "no mixing" und "large-mu" werden untere Grenzen auf die Higgs Boson Massen von mh > 84.5 GeV und mA > 86.3 GeV fuer tan(beta) > 0.7 abgeleitet. Weiterhin werden im "mh-max" Szenario 0.55 < tan(beta) < 2.2, im "no mixing" Szenario 0.4 < tan(beta) < 4.9, und im "large-mu" Szenario 0.7 < tan(beta) < 6.2 ausgeschlossen. Eine modellunabhaengige Suche nach dem Prozess e+e- -> hZ wird fuer den vier-Jet Endzustand durchgefuehrt. In Kombination mit den Ergebnissen von den anderen Kanaelen werden Grenzen fuer die hZZ Kopplung bestimmt. Wird die hZZ Kopplung auf den Wert im Standard Modell gesetzt und der Zerfall des Higgs Bosons zu 100% in Hadronen angenommen, ergibt sich als Grenze der Higgs Boson Masse, mh > 97 GeV. Modellunabhaengige obere Grenzen fuer die hAZ Kopplung werden aus der Suche nach der Paarerzeugung von Higgs Bosonen in den Kanaelen hA->qqqq und hA->qq tau+tau- in Abhaengigkeit von den Higgs Boson Massen abgeleitet. Die Resultate aus der Kombination aller LEP Experimente werden fuer die oben genannten Analysen vorgestellt. Die Perspektiven der Higgs Boson Suche an den TEVATRON und LHC Speicherringen werden diskutiert und die Higgs Boson Physik an kuenftigen e+e- Linearbeschleunigern behandelt. Ein Linearbeschleuniger wie TESLA waere ideal fuer Untersuchungen eines leichten Higgs Bosons. Fuer ein Higgs Boson mit einer Masse zwischen 120 und 180 GeV kann mH mit einer Praezision von 40 bis 70 MeV bestimmt werden. Im gleichen Massenbereich ist die Messung des Wirkungsquerschnitts, weitgehend modellunabhaengig, mit einem relativen Fehler von 2.6 bis 3.8% moeglich. In vier-Fermion und sechs-Fermion Endzustaenden werden topologische Wirkungsquerschnitte, definiert als Produkt des totalen Wirkungsquerschnitts fuer e+e- -> HZ mit dem Verzweigungsverhaeltnis eines Zerfallskanals, untersucht. Fuer den Messfehler werden 1.1% fuer HZ->bbqq und 13% fuer HZ->W+W-l+l- bei mH = 120 GeV abgeschaetzt. Die Gesamtheit dieser und weiterer Messungen erlaubt eine genaue Bestimmung des Higgs Boson Profils und gibt Aufschluss ueber die Struktur des Higgs Sektors in der Natur. / This thesis is devoted to the search for neutral Higgs bosons predicted by various theoretical models. The Higgs boson arises as a result of spontaneous breaking of SU(2) symmetry leading to the generation of masses of fermions and weak bosons. The search is done in all experimentally related channels using the data collected at center-of-mass energies up to 209 GeV in the years 1998-2000 with the L3 detector at the Large Electron Positron collider, LEP. Here the study of the final states characterised by four jets is described in detail. For other final states the analyses are briefly reviewed and the results are reported. The data are compared with the expectation from the Standard Model background processes and with various signal hypotheses. A model independent search for neutral Higgs bosons is also performed. No evidence for the production of Higgs bosons is found. New mass limits are determined superseding previous mass limits established by L3 and other experiments. First I describe the analysis searching for the Standard Model Higgs Boson. Its production at LEP is expected mainly via the Higgs-strahlung process. In the mass range accessible at LEP the Standard Model Higgs Boson is predicted to decay dominantly into a pair of b and anti-b quarks, hence the dedicated analyses are optimised for the H->bb decay mode. The four-jet signal topology is investigated and then combined with the other search channels leading to a lower mass limit of mH > 112.0 GeV at 95% C.L.. The results of the search are also interpreted in terms of limits on the HZZ coupling. In the Minimal Supersymmetric Standard Model (MSSM) the Higgs sector is extended to five physical states. The Higgs-strahlung process is complemented by the mechanism of the Higgs boson pair production e+e- -> hA. Therefore, for the interpretation of the results in the framework of the MSSM the Standard Model analyses are combined with the hA -> bb tau+tau-, hA -> bbbb and hZ->AAqq channels. Three benchmark MSSM scenarios denoted "mh-max", "no mixing" and "large-mu" are considered. Using L3 data the lower bounds on the Higgs boson masses mh > 84.5 GeV mA > 86.3 GeV are derived at 95% C.L. for tan(beta) > 0.7. For the "mh-max", "no mixing" and "large-mu" scenarios, ranges 0.55 < tan(beta) < 2.2, 0.4 < tan(beta) < 4.9 and 0.7 < tan(beta) < 6.2, respectively, are ruled out. A model independent search for the Higgs-strahlung process with subsequent decay of h into hadrons is carried out in the four-jet channel. The results of the analysis are then combined with the other channels. A limit on the hZZ coupling as a function of the Higgs boson mass is derived. The results of L3 combined search establish a 95% C.L. lower mass limit, mh > 97 GeV, for a hadronically decaying Higgs boson assuming the cross section of the Higgs-strahlung process to be equal to the value predicted by the Standard Model and the branching fraction of the Higgs boson into hadrons equal to 100%. Analyses are developed to search exclusively for the hA -> bbbb, hA -> qqqq, hA -> bb tau+tau- and hA -> qq tau+tau- final states. Results of these analyses are translated into a 95% C.L. upper limit on the hAZ coupling as a function of Higgs boson masses. Searches for neutral Higgs bosons carried out by the L3 collaboration are combined with searches performed in other LEP experiments. The results of this combination are reported. The perspectives of Higgs boson searches at TEVATRON and LHC are briefly reviewed. The prospects of Higgs physics at a future linear e+e- collider are discussed. The potential of the TESLA detector foreseen at the TESLA linear collider for the determination of Higgs boson properties is studied. The Higgs boson masses 120, 150 and 180 GeV are considered. It is shown that a precision of 40 - 70 MeV in the measurement of the Higgs boson mass can be achieved. A model independent method to measure the e+e- -> HZ cross section is proposed. The method is based on the study of the inclusive HZ -> X e+e- and X mu+mu- channels. The relative error in the determination of the cross section varies between 2.6% and 3.8% for Higgs boson mass ranging from 120 GeV to 180 GeV. For the four-fermion and six-fermion final states arising from the Higgs-strahlung process the accuracy of the measurement of a topological cross section, defined as the product of the Higgs-strahlung cross section and the branching fraction of the specific final state, is investigated. The relative uncertainty of this measurement varies from 1.1% and 13%, depending on final state and Higgs boson mass. These and other measurements will allow to determine the profile of the Higgs boson and give insight into the structure of the Higgs sector in nature.

Die Dynamik anfänglich aus dem Gleichgewicht gebrachter wechselwirkender Quantenvielteilchensysteme wirft aktuell noch spannende Fragen auf. In Bezug auf die Thermalisierung ist z.B. nach wie vor ungeklärt, in welcher Form sie überhaupt stattfindet und in welchen Observablen bzw. auf welcher Zeitskala sie zu beobachten ist. Eine ideale Grundlage zur Erforschung von Relaxationsdynamiken in wechselwirkenden Vielteilchensystemen bieten ultrakalte Quantengase aufgrund ihrer guten Kontrollier- und Variierbarkeit. Ein allgemeiner theoretischer Rahmen, auf dessen Basis solche Prozesse zu untersuchen sind, steht jedoch infolge der großen Anzahl der beteiligten Freiheitsgrade bisher nicht zur Verfügung. Für ultrakalte bosonische Gase stellt die Gross-Pitaevskii-Gleichung eines der wichtigsten theoretischen Werkzeuge dar, eine klassische Feldgleichung für die Kondensatwellenfunktion in Molekularfeldnäherung. Die ihr zugrunde liegende Näherung erlaubt jedoch keine nicht-trivialen Aussagen über den vollen N-Teilchenzustand, dessen Kenntnis für die Untersuchung einer möglichen Relaxationsdynamik unabdingbar ist. Um der theoretischen Beschreibung des vollen bosonischen Feldes einen Schritt näher zu kommen, untersucht die vorliegende Arbeit die Anwendung semiklassischer Methoden auf ultrakalte Bosegase. Diese sind in der Regel dann sehr genau, wenn die beteiligten Wirkungen groß gegenüber dem Planckschen Wirkungsquantum sind. Für bosonische Felder wird dieser Grenzfall durch die Bedingung einer großen Teilchenzahl ersetzt. Die immense Anzahl an Teilchen in den hier behandelten Vielteilchensystemen macht die Anwendung semiklassischer Methoden auf diesem Gebiet also vielversprechend. Als zentrales Modellsystem wird ein anfänglich aus dem Gleichgewicht gebrachtes ultrakaltes bosonisches Doppelmuldensystem betrachtet, das eine hochinteressante Dynamik aufweist, die auf das Wechselspiel der Tunneldynamik einerseits und der Wechselwirkung der Teilchen untereinander andererseits zurückzuführen ist. Als Referenz lassen sich aufgrund der speziellen Fallengeometrie im Rahmen der Zwei-Moden-Näherung die Ergebnisse einer numerisch exakten Untersuchung heranziehen. Durch den Einsatz der namhaften WKB-Quantisierung und des besonders aus der Molekülphysik bekannten Reflexionsprinzips wird hier ein geschlossener analytischer Ausdruck für die sogenannte Populationsdifferenz im Doppelminimum hergeleitet, der ausschließlich von den wenigen relevanten Systemparametern abhängt. Diese mächtige Formel erlaubt es nun zum ersten Mal, in quantitativer Weise die charakteristische Sequenz aus Oszillationen, Kollapsen und Revivals in Abhängigkeit der vorausgesetzten Parameter zu untersuchen. Nach dieser ersten erfolgreichen Anwendung semiklassischer Methoden im Modellsystem wird über die reduzierte Dynamik der Populationsdifferenz hinausgegangen. Mithilfe des semiklassischen Herman-Kluk-Propagators lässt sich selbst der volle N-Teilchenzustand untersuchen. Da es letztlich um die Beschreibung ultrakalter Bosonen in beliebigen Potentialen gehen soll, wird zunächst der Herman-Kluk-Propagator für eine Feldtheorie vorgestellt. Im Doppelmuldensystem zeigt sich dann in der Anwendung die semiklassische Propagation in der Lage, für alle untersuchten Parameterregime gute Übereinstimmung mit den numerisch exakten Ergebnissen zu liefern. Zusätzlich findet ein Abgleich der Resultate mit der Truncated Wigner Approximation statt, auf die im Forschungsgebiet ultrakalter Bosonen häufig zurück gegriffen wird. Diese beschreibt die Zeitentwicklung einer Wignerverteilung unter Aussparung der Quanteninterferenzen. In der vorliegenden Arbeit wird gezeigt, dass die Herman-Kluk-Propagation unter Berücksichtigung der Phasen weit über die Truncated Wigner Approximation hinausgeht: Sie gibt alle wichtigen Charakteristika der Dynamik im Doppelmuldensystem wieder. Um die Semiklassik auf ihre Aussagefähigkeit in Bezug auf eine noch komplexere Dynamik zu untersuchen, wird zum Abschluss das Drei-Topf-System betrachtet, das zusätzlich chaotische Regionen im Phasenraum aufweist. Auch hier zeigt sich, dass die semiklassische Berücksichtigung der Phasen die Truncated Wigner Approximation in den Schatten stellt. Allerdings ergeben sich durch die Instabilität der Trajektorien für stark chaotische Regime numerische Probleme, die es in der Zukunft zu lösen gilt. / The dynamics of initially non equilibrium interacting quantum many body systems is an ongoing and interesting field of research. It is still an open question in which form relaxation occurs in such systems, and in which observables and on which timescales a possible thermalization might appear. A perfect playground for the investigations of relaxation dynamics in interacting many body schemes is provided by ultracold quantum gases, which are easily to be controlled and varied in experiments. However, a general theoretical framework for the investigation of such processes is still missing, due to the huge amount of involved degrees of freedom. One of the main theoretical tools in the field of ultracold bosonic gases represents the famous Gross-Pitaevskii equation, a field equation for the Bose-Einstein condensate wave function in terms of a mean-field approximation. However, the underlying approximation prevents the possibility to draw non-trivial conclusions about the full N-particle state, the information of which is necessary for the analysis of relaxation processes. To gain the theoretical description of the full bosonic field, the present thesis deals with the application of semiclassical methods to ultracold boson gases. Those techniques become in general exact, as long as the involved actions are large compared to Planck's constant. For many body systems it turns out that semiclassics are expected to give good results also for the condition of high particle numbers, which is precisely fulfilled in these schemes, making the semiclassical approaches promising. As an essential model system an initially out of equilibrium ultracold bosonic double-well system is investigated. This configuration provides highly interesting dynamics due to the interplay of the tunneling dynamics on the one hand and the interaction amongst the particles on the other. The special trap geometry makes exact numerical calculations in the framework of the two-mode approximation available, which serve in the following as reference data. By applying the common semiclassical WKB approximation and the reflection principle known from molecule physics, a closed analytical expression for the so-called population imbalance of the bosons in the double-well is derived, depending only on the few relevant system parameters. This mighty formula allows for the first time the quantitative investigation of the characteristic sequence consisting of oscillations, collapse and revivals in dependence on the parameters of the system. Since the semiclassical approaches succeeded for the double-well model so far the so-called Herman-Kluk propagator is adopted, to go beyond the reduced dynamics of the population imbalance. The propagator provides the possibility to treat the full N-particle state theoretically and is introduced for the most general case of a bosonic quantum field. Its application to the double-well system yields for all investigated parameter regimes very good agreement with the numerical exact results. Furthermore the outcomes are compared to the Truncated Wigner approximation, which is frequently used in the research field of ultracold bosons. This approach pictures the time evolution of a Wigner distribution, without taking into account the quantum interferences. In the present thesis it is shown that the Herman-Kluk propagation goes clearly beyond the truncated Wigner approach by considering in addition the quantum phases: The propagator is able to reproduce all of the distinctive features of the double-well dynamics. In order to test the performance of semiclassical methods in matters of even more complex systems, the ultracold bosonic triple-well model is finally considered, which exhibits unlike the double-well scheme chaotic regions in phase space. It turns out that the semiclassical propagation outplays again the truncated Wigner approximation. On the other hand the instability of the highly chaotic trajectories causes numerical problems, which have to be solved in the future.

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.

Die Dynamik anfänglich aus dem Gleichgewicht gebrachter wechselwirkender Quantenvielteilchensysteme wirft aktuell noch spannende Fragen auf. In Bezug auf die Thermalisierung ist z.B. nach wie vor ungeklärt, in welcher Form sie überhaupt stattfindet und in welchen Observablen bzw. auf welcher Zeitskala sie zu beobachten ist. Eine ideale Grundlage zur Erforschung von Relaxationsdynamiken in wechselwirkenden Vielteilchensystemen bieten ultrakalte Quantengase aufgrund ihrer guten Kontrollier- und Variierbarkeit. Ein allgemeiner theoretischer Rahmen, auf dessen Basis solche Prozesse zu untersuchen sind, steht jedoch infolge der großen Anzahl der beteiligten Freiheitsgrade bisher nicht zur Verfügung. Für ultrakalte bosonische Gase stellt die Gross-Pitaevskii-Gleichung eines der wichtigsten theoretischen Werkzeuge dar, eine klassische Feldgleichung für die Kondensatwellenfunktion in Molekularfeldnäherung. Die ihr zugrunde liegende Näherung erlaubt jedoch keine nicht-trivialen Aussagen über den vollen N-Teilchenzustand, dessen Kenntnis für die Untersuchung einer möglichen Relaxationsdynamik unabdingbar ist. Um der theoretischen Beschreibung des vollen bosonischen Feldes einen Schritt näher zu kommen, untersucht die vorliegende Arbeit die Anwendung semiklassischer Methoden auf ultrakalte Bosegase. Diese sind in der Regel dann sehr genau, wenn die beteiligten Wirkungen groß gegenüber dem Planckschen Wirkungsquantum sind. Für bosonische Felder wird dieser Grenzfall durch die Bedingung einer großen Teilchenzahl ersetzt. Die immense Anzahl an Teilchen in den hier behandelten Vielteilchensystemen macht die Anwendung semiklassischer Methoden auf diesem Gebiet also vielversprechend. Als zentrales Modellsystem wird ein anfänglich aus dem Gleichgewicht gebrachtes ultrakaltes bosonisches Doppelmuldensystem betrachtet, das eine hochinteressante Dynamik aufweist, die auf das Wechselspiel der Tunneldynamik einerseits und der Wechselwirkung der Teilchen untereinander andererseits zurückzuführen ist. Als Referenz lassen sich aufgrund der speziellen Fallengeometrie im Rahmen der Zwei-Moden-Näherung die Ergebnisse einer numerisch exakten Untersuchung heranziehen. Durch den Einsatz der namhaften WKB-Quantisierung und des besonders aus der Molekülphysik bekannten Reflexionsprinzips wird hier ein geschlossener analytischer Ausdruck für die sogenannte Populationsdifferenz im Doppelminimum hergeleitet, der ausschließlich von den wenigen relevanten Systemparametern abhängt. Diese mächtige Formel erlaubt es nun zum ersten Mal, in quantitativer Weise die charakteristische Sequenz aus Oszillationen, Kollapsen und Revivals in Abhängigkeit der vorausgesetzten Parameter zu untersuchen. Nach dieser ersten erfolgreichen Anwendung semiklassischer Methoden im Modellsystem wird über die reduzierte Dynamik der Populationsdifferenz hinausgegangen. Mithilfe des semiklassischen Herman-Kluk-Propagators lässt sich selbst der volle N-Teilchenzustand untersuchen. Da es letztlich um die Beschreibung ultrakalter Bosonen in beliebigen Potentialen gehen soll, wird zunächst der Herman-Kluk-Propagator für eine Feldtheorie vorgestellt. Im Doppelmuldensystem zeigt sich dann in der Anwendung die semiklassische Propagation in der Lage, für alle untersuchten Parameterregime gute Übereinstimmung mit den numerisch exakten Ergebnissen zu liefern. Zusätzlich findet ein Abgleich der Resultate mit der Truncated Wigner Approximation statt, auf die im Forschungsgebiet ultrakalter Bosonen häufig zurück gegriffen wird. Diese beschreibt die Zeitentwicklung einer Wignerverteilung unter Aussparung der Quanteninterferenzen. In der vorliegenden Arbeit wird gezeigt, dass die Herman-Kluk-Propagation unter Berücksichtigung der Phasen weit über die Truncated Wigner Approximation hinausgeht: Sie gibt alle wichtigen Charakteristika der Dynamik im Doppelmuldensystem wieder. Um die Semiklassik auf ihre Aussagefähigkeit in Bezug auf eine noch komplexere Dynamik zu untersuchen, wird zum Abschluss das Drei-Topf-System betrachtet, das zusätzlich chaotische Regionen im Phasenraum aufweist. Auch hier zeigt sich, dass die semiklassische Berücksichtigung der Phasen die Truncated Wigner Approximation in den Schatten stellt. Allerdings ergeben sich durch die Instabilität der Trajektorien für stark chaotische Regime numerische Probleme, die es in der Zukunft zu lösen gilt. / The dynamics of initially non equilibrium interacting quantum many body systems is an ongoing and interesting field of research. It is still an open question in which form relaxation occurs in such systems, and in which observables and on which timescales a possible thermalization might appear. A perfect playground for the investigations of relaxation dynamics in interacting many body schemes is provided by ultracold quantum gases, which are easily to be controlled and varied in experiments. However, a general theoretical framework for the investigation of such processes is still missing, due to the huge amount of involved degrees of freedom. One of the main theoretical tools in the field of ultracold bosonic gases represents the famous Gross-Pitaevskii equation, a field equation for the Bose-Einstein condensate wave function in terms of a mean-field approximation. However, the underlying approximation prevents the possibility to draw non-trivial conclusions about the full N-particle state, the information of which is necessary for the analysis of relaxation processes. To gain the theoretical description of the full bosonic field, the present thesis deals with the application of semiclassical methods to ultracold boson gases. Those techniques become in general exact, as long as the involved actions are large compared to Planck's constant. For many body systems it turns out that semiclassics are expected to give good results also for the condition of high particle numbers, which is precisely fulfilled in these schemes, making the semiclassical approaches promising. As an essential model system an initially out of equilibrium ultracold bosonic double-well system is investigated. This configuration provides highly interesting dynamics due to the interplay of the tunneling dynamics on the one hand and the interaction amongst the particles on the other. The special trap geometry makes exact numerical calculations in the framework of the two-mode approximation available, which serve in the following as reference data. By applying the common semiclassical WKB approximation and the reflection principle known from molecule physics, a closed analytical expression for the so-called population imbalance of the bosons in the double-well is derived, depending only on the few relevant system parameters. This mighty formula allows for the first time the quantitative investigation of the characteristic sequence consisting of oscillations, collapse and revivals in dependence on the parameters of the system. Since the semiclassical approaches succeeded for the double-well model so far the so-called Herman-Kluk propagator is adopted, to go beyond the reduced dynamics of the population imbalance. The propagator provides the possibility to treat the full N-particle state theoretically and is introduced for the most general case of a bosonic quantum field. Its application to the double-well system yields for all investigated parameter regimes very good agreement with the numerical exact results. Furthermore the outcomes are compared to the Truncated Wigner approximation, which is frequently used in the research field of ultracold bosons. This approach pictures the time evolution of a Wigner distribution, without taking into account the quantum interferences. In the present thesis it is shown that the Herman-Kluk propagation goes clearly beyond the truncated Wigner approach by considering in addition the quantum phases: The propagator is able to reproduce all of the distinctive features of the double-well dynamics. In order to test the performance of semiclassical methods in matters of even more complex systems, the ultracold bosonic triple-well model is finally considered, which exhibits unlike the double-well scheme chaotic regions in phase space. It turns out that the semiclassical propagation outplays again the truncated Wigner approximation. On the other hand the instability of the highly chaotic trajectories causes numerical problems, which have to be solved in the future.

The discovery of a heavy neutral particle would be a direct hint for new physics beyond the Standard Model. In this thesis searches for new heavy neutral particles decaying into two tau leptons, which further decay into hadrons, are presented. They cover neutral Higgs bosons in the context of the minimal supersymmetric extension of the Standard Model (MSSM) as well as Z′ bosons, predicted by various theories with an extended gauge sector. Both analyses are based on the full 2012 proton-proton collision dataset taken by the ATLAS experiment at the Large Hadron Collider (LHC). The extended Higgs sector in the MSSM suggests additional heavy neutral Higgs bosons which decay into tau leptons in about 10% of the time. Given that the dominant final state, φ → b¯b, suffers from tremendous QCD initiated backgrounds, the decay into two tau leptons is the most promising final state to discover such new resonances. The fully hadronic final state is the dominant one with a branching fraction of about 42%. It governs the sensitivity, in particular at high transverse momentum when the QCD multijet background becomes small. Other theoretical extensions of the Standard Model, which are mainly driven by the concept of gauge unification, predict additional heavy particles arising from an extended underlying gauge group. Some of them further predict an enhanced coupling to fermions of the third generation. This motivates the search for Z′ bosons in the fully hadronic di-tau final state. One major challenge in physics analyses involving tau leptons is to have an outstanding performance of trigger and identification algorithms suitable to select real tau leptons with high efficiency, while rejecting fake taus originating from quark or gluon initiated jets. In this work a new tau trigger concept based on multivariate classifiers has been developed and became the default tau trigger algorithm in 2012 data-taking. An updated tau identification technique based on the log-likelihood approach has been provided for 2011 data-taking. Furthermore, a new framework has been developed to perform the tuning of the tau identification algorithm and exploited for the optimisation for 2012 data-taking, accordingly. The search for new heavy neutral Higgs bosons in the context of the MSSM has been performed exploiting the full 2012 dataset corresponding to an integrated luminosity of 19.5 fb−1 taken at a centre-of-mass energy of √s = 8 TeV. Updated event selection criteria and novel data-driven background estimation techniques have been developed and are suitable to increase the sensitivity of the analysis significantly. No deviations from the Standard Model prediction are observed, and thus 95% C.L. exclusion limits on the production cross section times branching ratio, σ(pp → φ) × BR(φ → ττ), are derived exploiting the CLs method. The exclusion ranges from 13.0 pb at 150GeV to 7.0 fb at 1 TeV for Higgs boson production in association with b-quarks and from 23.6 pb at 150GeV to 7.5 fb at 1 TeV for Higgs bosons produced via gluon-gluon fusion. The obtained exclusion limit on σ(pp → φ) × BR(φ → ττ) can be related to an exclusion of the MSSM parameter space in the MA-tan β-plane. Various benchmark scenario are considered. The ”standard candle” is the mhmax scenario, for which tan β values between 13.3 and 55 can be excluded at 95% C.L. in the considered mass range. Updated benchmark scenarios designed to incorporate the recently discovered SM-like Higgs boson were suggested and analysed as well. In the mhmod+ (mhmod−) scenario tan β values between 13.5 (13.3 ) and 55 (52 ) can be excluded. Finally, a search for heavy neutral resonances in the context of Z′ bosons was performed. As in the search for new Higgs bosons, no deviation from the Standard Model prediction is observed, and hence exclusion limits on the production cross section times branching ratio, σ(pp → Z′) × BR(Z′ → ττ), and on the Z′ boson mass are derived exploiting the Bayesian approach. Z′ bosons with MZ′ < 1.9 TeV can be excluded at 95% credibility, and thus mark the strongest exclusion limit obtained in the di-tau final state by any collider experiment so far.

The discovery of a heavy neutral particle would be a direct hint for new physics beyond the Standard Model. In this thesis searches for new heavy neutral particles decaying into two tau leptons, which further decay into hadrons, are presented. They cover neutral Higgs bosons in the context of the minimal supersymmetric extension of the Standard Model (MSSM) as well as Z′ bosons, predicted by various theories with an extended gauge sector. Both analyses are based on the full 2012 proton-proton collision dataset taken by the ATLAS experiment at the Large Hadron Collider (LHC). The extended Higgs sector in the MSSM suggests additional heavy neutral Higgs bosons which decay into tau leptons in about 10% of the time. Given that the dominant final state, φ → b¯b, suffers from tremendous QCD initiated backgrounds, the decay into two tau leptons is the most promising final state to discover such new resonances. The fully hadronic final state is the dominant one with a branching fraction of about 42%. It governs the sensitivity, in particular at high transverse momentum when the QCD multijet background becomes small. Other theoretical extensions of the Standard Model, which are mainly driven by the concept of gauge unification, predict additional heavy particles arising from an extended underlying gauge group. Some of them further predict an enhanced coupling to fermions of the third generation. This motivates the search for Z′ bosons in the fully hadronic di-tau final state. One major challenge in physics analyses involving tau leptons is to have an outstanding performance of trigger and identification algorithms suitable to select real tau leptons with high efficiency, while rejecting fake taus originating from quark or gluon initiated jets. In this work a new tau trigger concept based on multivariate classifiers has been developed and became the default tau trigger algorithm in 2012 data-taking. An updated tau identification technique based on the log-likelihood approach has been provided for 2011 data-taking. Furthermore, a new framework has been developed to perform the tuning of the tau identification algorithm and exploited for the optimisation for 2012 data-taking, accordingly. The search for new heavy neutral Higgs bosons in the context of the MSSM has been performed exploiting the full 2012 dataset corresponding to an integrated luminosity of 19.5 fb−1 taken at a centre-of-mass energy of √s = 8 TeV. Updated event selection criteria and novel data-driven background estimation techniques have been developed and are suitable to increase the sensitivity of the analysis significantly. No deviations from the Standard Model prediction are observed, and thus 95% C.L. exclusion limits on the production cross section times branching ratio, σ(pp → φ) × BR(φ → ττ), are derived exploiting the CLs method. The exclusion ranges from 13.0 pb at 150GeV to 7.0 fb at 1 TeV for Higgs boson production in association with b-quarks and from 23.6 pb at 150GeV to 7.5 fb at 1 TeV for Higgs bosons produced via gluon-gluon fusion. The obtained exclusion limit on σ(pp → φ) × BR(φ → ττ) can be related to an exclusion of the MSSM parameter space in the MA-tan β-plane. Various benchmark scenario are considered. The ”standard candle” is the mhmax scenario, for which tan β values between 13.3 and 55 can be excluded at 95% C.L. in the considered mass range. Updated benchmark scenarios designed to incorporate the recently discovered SM-like Higgs boson were suggested and analysed as well. In the mhmod+ (mhmod−) scenario tan β values between 13.5 (13.3 ) and 55 (52 ) can be excluded. Finally, a search for heavy neutral resonances in the context of Z′ bosons was performed. As in the search for new Higgs bosons, no deviation from the Standard Model prediction is observed, and hence exclusion limits on the production cross section times branching ratio, σ(pp → Z′) × BR(Z′ → ττ), and on the Z′ boson mass are derived exploiting the Bayesian approach. Z′ bosons with MZ′ < 1.9 TeV can be excluded at 95% credibility, and thus mark the strongest exclusion limit obtained in the di-tau final state by any collider experiment so far.