Holographic field theory models of dark energy in interaction with dark matter

We discuss two Lagrangian interacting dark energy models in the context of the holographic principle. The potentials of the interacting fields are constructed. The models are compared with CMB distance information, baryonic acoustic oscillations, lookback time and the Constitution supernovae sample. For both models, the results are consistent with a nonvanishing interaction in the dark sector of the Universe and the sign of coupling is consistent with dark energy decaying into dark matter, alleviating the coincidence problem-with more than 3 standard deviations of confidence for one of them. However, this is because the noninteracting holographic dark energy model is a bad fit to the combination of data sets used in this work as compared to the cosmological constant with cold dark matter model, so that one needs to introduce the interaction in order to improve this model.

All-loop finiteness of the two-dimensional noncommutative supersymmetric gauge theory

Within the superfield approach, we discuss the two-dimensional noncommutative super-QED. Its all-order finiteness is explicitly shown. Copyright (C) EPLA, 2012

Magnetic hyperthermia investigation of cobalt ferrite nanoparticles: Comparison between experiment, linear response theory, and dynamic hysteresis simulations

Considerable effort has been made in recent years to optimize materials properties for magnetic hyperthermia applications. However, due to the complexity of the problem, several aspects pertaining to the combined influence of the different parameters involved still remain unclear. In this paper, we discuss in detail the role of the magnetic anisotropy on the specific absorption rate of cobalt-ferrite nanoparticles with diameters ranging from 3 to 14 nm. The structural characterization was carried out using x-ray diffraction and Rietveld analysis and all relevant magnetic parameters were extracted from vibrating sample magnetometry. Hyperthermia investigations were performed at 500 kHz with a sinusoidal magnetic field amplitude of up to 68 Oe. The specific absorption rate was investigated as a function of the coercive field, saturation magnetization, particle size, and magnetic anisotropy. The experimental results were also compared with theoretical predictions from the linear response theory and dynamic hysteresis simulations, where exceptional agreement was found in both cases. Our results show that the specific absorption rate has a narrow and pronounced maxima for intermediate anisotropy values. This not only highlights the importance of this parameter but also shows that in order to obtain optimum efficiency in hyperthermia applications, it is necessary to carefully tailor the materials properties during the synthesis process. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729271]

Application of H∞ theory to a 6 DOF flight simulator motion base

The purpose of this study is to apply inverse dynamics control for a six degree of freedom flight simulator motion system. Imperfect compensation of the inverse dynamic control is intentionally introduced in order to simplify the implementation of this approach. The control strategy is applied in the outer loop of the inverse dynamic control to counteract the effects of imperfect compensation. The control strategy is designed using H∞ theory. Forward and inverse kinematics and full dynamic model of a six degrees of freedom motion base driven by electromechanical actuators are briefly presented. Describing function, acceleration step response and some maneuvers computed from the washout filter were used to evaluate the performance of the controllers.

Bioremediation of PAHs - Limitations and soultions

Introduction 1.1 Occurrence of polycyclic aromatic hydrocarbons (PAH) in the environment Worldwide industrial and agricultural developments have released a large number of natural and synthetic hazardous compounds into the environment due to careless waste disposal, illegal waste dumping and accidental spills. As a result, there are numerous sites in the world that require cleanup of soils and groundwater. Polycyclic aromatic hydrocarbons (PAHs) are one of the major groups of these contaminants (Da Silva et al., 2003). PAHs constitute a diverse class of organic compounds consisting of two or more aromatic rings with various structural configurations (Prabhu and Phale, 2003). Being a derivative of benzene, PAHs are thermodynamically stable. In addition, these chemicals tend to adhere to particle surfaces, such as soils, because of their low water solubility and strong hydrophobicity, and this results in greater persistence under natural conditions. This persistence coupled with their potential carcinogenicity makes PAHs problematic environmental contaminants (Cerniglia, 1992; Sutherland, 1992). PAHs are widely found in high concentrations at many industrial sites, particularly those associated with petroleum, gas production and wood preserving industries (Wilson and Jones, 1993). 1.2 Remediation technologies Conventional techniques used for the remediation of soil polluted with organic contaminants include excavation of the contaminated soil and disposal to a landfill or capping - containment - of the contaminated areas of a site. These methods have some drawbacks. The first method simply moves the contamination elsewhere and may create significant risks in the excavation, handling and transport of hazardous material. Additionally, it is very difficult and increasingly expensive to find new landfill sites for the final disposal of the material. The cap and containment method is only an interim solution since the contamination remains on site, requiring monitoring and maintenance of the isolation barriers long into the future, with all the associated costs and potential liability. A better approach than these traditional methods is to completely destroy the pollutants, if possible, or transform them into harmless substances. Some technologies that have been used are high-temperature incineration and various types of chemical decomposition (for example, base-catalyzed dechlorination, UV oxidation). However, these methods have significant disadvantages, principally their technological complexity, high cost , and the lack of public acceptance. Bioremediation, on the contrast, is a promising option for the complete removal and destruction of contaminants. 1.3 Bioremediation of PAH contaminated soil & groundwater Bioremediation is the use of living organisms, primarily microorganisms, to degrade or detoxify hazardous wastes into harmless substances such as carbon dioxide, water and cell biomass Most PAHs are biodegradable unter natural conditions (Da Silva et al., 2003; Meysami and Baheri, 2003) and bioremediation for cleanup of PAH wastes has been extensively studied at both laboratory and commercial levels- It has been implemented at a number of contaminated sites, including the cleanup of the Exxon Valdez oil spill in Prince William Sound, Alaska in 1989, the Mega Borg spill off the Texas coast in 1990 and the Burgan Oil Field, Kuwait in 1994 (Purwaningsih, 2002). Different strategies for PAH bioremediation, such as in situ , ex situ or on site bioremediation were developed in recent years. In situ bioremediation is a technique that is applied to soil and groundwater at the site without removing the contaminated soil or groundwater, based on the provision of optimum conditions for microbiological contaminant breakdown.. Ex situ bioremediation of PAHs, on the other hand, is a technique applied to soil and groundwater which has been removed from the site via excavation (soil) or pumping (water). Hazardous contaminants are converted in controlled bioreactors into harmless compounds in an efficient manner. 1.4 Bioavailability of PAH in the subsurface Frequently, PAH contamination in the environment is occurs as contaminants that are sorbed onto soilparticles rather than in phase (NAPL, non aqueous phase liquids). It is known that the biodegradation rate of most PAHs sorbed onto soil is far lower than rates measured in solution cultures of microorganisms with pure solid pollutants (Alexander and Scow, 1989; Hamaker, 1972). It is generally believed that only that fraction of PAHs dissolved in the solution can be metabolized by microorganisms in soil. The amount of contaminant that can be readily taken up and degraded by microorganisms is defined as bioavailability (Bosma et al., 1997; Maier, 2000). Two phenomena have been suggested to cause the low bioavailability of PAHs in soil (Danielsson, 2000). The first one is strong adsorption of the contaminants to the soil constituents which then leads to very slow release rates of contaminants to the aqueous phase. Sorption is often well correlated with soil organic matter content (Means, 1980) and significantly reduces biodegradation (Manilal and Alexander, 1991). The second phenomenon is slow mass transfer of pollutants, such as pore diffusion in the soil aggregates or diffusion in the organic matter in the soil. The complex set of these physical, chemical and biological processes is schematically illustrated in Figure 1. As shown in Figure 1, biodegradation processes are taking place in the soil solution while diffusion processes occur in the narrow pores in and between soil aggregates (Danielsson, 2000). Seemingly contradictory studies can be found in the literature that indicate the rate and final extent of metabolism may be either lower or higher for sorbed PAHs by soil than those for pure PAHs (Van Loosdrecht et al., 1990). These contrasting results demonstrate that the bioavailability of organic contaminants sorbed onto soil is far from being well understood. Besides bioavailability, there are several other factors influencing the rate and extent of biodegradation of PAHs in soil including microbial population characteristics, physical and chemical properties of PAHs and environmental factors (temperature, moisture, pH, degree of contamination). Figure 1: Schematic diagram showing possible rate-limiting processes during bioremediation of hydrophobic organic contaminants in a contaminated soil-water system (not to scale) (Danielsson, 2000). 1.5 Increasing the bioavailability of PAH in soil Attempts to improve the biodegradation of PAHs in soil by increasing their bioavailability include the use of surfactants , solvents or solubility enhancers.. However, introduction of synthetic surfactant may result in the addition of one more pollutant. (Wang and Brusseau, 1993).A study conducted by Mulder et al. showed that the introduction of hydropropyl-ß-cyclodextrin (HPCD), a well-known PAH solubility enhancer, significantly increased the solubilization of PAHs although it did not improve the biodegradation rate of PAHs (Mulder et al., 1998), indicating that further research is required in order to develop a feasible and efficient remediation method. Enhancing the extent of PAHs mass transfer from the soil phase to the liquid might prove an efficient and environmentally low-risk alternative way of addressing the problem of slow PAH biodegradation in soil.

Transportation theory and planning

The aim of this research is to analyze the transport system and its subcomponents in order to highlight which are the design tools for physical and/or organizational projects related to transport supply systems. A characteristic of the transport systems is that the change of their structures can recoil on several entities, groups of entities, which constitute the community. The construction of a new infrastructure can modify both the transport service characteristic for all the user of the entire network; for example, the construction of a transportation infrastructure can change not only the transport service characteristics for the users of the entire network in which it is part of, but also it produces economical, social, and environmental effects. Therefore, the interventions or the improvements choices must be performed using a rational decision making approach. This approach requires that these choices are taken through the quantitative evaluation of the different effects caused by the different intervention plans. This approach becomes even more necessary when the decisions are taken in behalf of the community. Then, in order to understand how to develop a planning process in Transportation I will firstly analyze the transport system and the mathematical models used to describe it: these models provide us significant indicators which can be used to evaluate the effects of possible interventions. In conclusion, I will move on the topics related to the transport planning, analyzing the planning process, and the variables that have to be considered to perform a feasibility analysis or to compare different alternatives. In conclusion I will perform a preliminary analysis of a new transit system which is planned to be developed in New York City.

Higher-Order Concurrency: Expressiveness and Decidability Results

Higher-order process calculi are formalisms for concurrency in which processes can be passed around in communications. Higher-order (or process-passing) concurrency is often presented as an alternative paradigm to the first order (or name-passing) concurrency of the pi-calculus for the description of mobile systems. These calculi are inspired by, and formally close to, the lambda-calculus, whose basic computational step ---beta-reduction--- involves term instantiation. The theory of higher-order process calculi is more complex than that of first-order process calculi. This shows up in, for instance, the definition of behavioral equivalences. A long-standing approach to overcome this burden is to define encodings of higher-order processes into a first-order setting, so as to transfer the theory of the first-order paradigm to the higher-order one. While satisfactory in the case of calculi with basic (higher-order) primitives, this indirect approach falls short in the case of higher-order process calculi featuring constructs for phenomena such as, e.g., localities and dynamic system reconfiguration, which are frequent in modern distributed systems. Indeed, for higher-order process calculi involving little more than traditional process communication, encodings into some first-order language are difficult to handle or do not exist. We then observe that foundational studies for higher-order process calculi must be carried out directly on them and exploit their peculiarities. This dissertation contributes to such foundational studies for higher-order process calculi. We concentrate on two closely interwoven issues in process calculi: expressiveness and decidability. Surprisingly, these issues have been little explored in the higher-order setting. Our research is centered around a core calculus for higher-order concurrency in which only the operators strictly necessary to obtain higher-order communication are retained. We develop the basic theory of this core calculus and rely on it to study the expressive power of issues universally accepted as basic in process calculi, namely synchrony, forwarding, and polyadic communication.

Reconstructing Quantum Field Theory from an Educational Perspective

The research work concerns the analysis of the foundations of Quantum Field Theory carried out from an educational perspective. The whole research has been driven by two questions: • How the concept of object changes when moving from classical to contemporary physics? • How are the concepts of field and interaction shaped and conceptualized within contemporary physics? What makes quantum field and interaction similar to and what makes them different from the classical ones? The whole work has been developed through several studies: 1. A study aimed to analyze the formal and conceptual structures characterizing the description of the continuous systems that remain invariant in the transition from classical to contemporary physics. 2. A study aimed to analyze the changes in the meanings of the concepts of field and interaction in the transition to quantum field theory. 3. A detailed study of the Klein-Gordon equation aimed at analyzing, in a case considered emblematic, some interpretative (conceptual and didactical) problems in the concept of field that the university textbooks do not address explicitly. 4. A study concerning the application of the “Discipline-Culture” Model elaborated by I. Galili to the analysis of the Klein-Gordon equation, in order to reconstruct the meanings of the equation from a cultural perspective. 5. A critical analysis, in the light of the results of the studies mentioned above, of the existing proposals for teaching basic concepts of Quantum Field Theory and particle physics at the secondary school level or in introductory physics university courses.

La sostenibilità organizzativa dei progetti agricoli di cooperazione internazionale allo sviluppo

The importance of organizational issues to assess the success of international development project has not been fully considered yet. After a brief overview, in 1st chapter, on main actors involved on international cooperation, in the 2nd chapter an analysis of the literature on the project success definition, focused on the success criteria and success factors, was carried out by surveying the contribution of different authors and approaches. Traditionally projects were perceived as successful when they met time, budget and performance goals, assuming a basic similarity among projects (universalistic approach). However, starting from a non-universalistic approach, the importance of organization’s effectiveness, in terms of Relations Sustainability, emerged as a dimension able to define and assess a project success. The identification of the factors influencing the relationship between and inside the organizations becomes consequently a priority. In 3th chapter, starting from a literature survey, the different analytical approaches related to the inter and intra-organization relationships are analysed. They involve two different groups: the first includes studies focused on the type of organizations relationship structure (Supply Chains, Networks, Clusters and Industrial Districts); the second group includes approaches related to the general theories on firms relationship interpretation (Transaction Costs Economics, Resource Based View, Organization Theory). The variables and logical frameworks provided by these different theoretical contributions are compared and classified in order to find out possible connections and/or juxtapositions. Being an exhaustive collection of the literature on the subject is impossible, the main goal is to underline the existence of potentially overlapping and/or integrating approaches examining the contribution provided by different representative authors. The survey showed first of all many variables in common between approaches coming from different disciplines; furthermore the non overlapping variables can be integrated contributing to a broader picture of the variables influencing the organization relations; in particular a theoretical design for the identification of connections between the inter and the intra-organizations relations was made possible. The results obtained in 3th chapter help to defining a general theoretical framework linking the different interpretative variables. Based on extensive research contributions on the factors influencing the relations between organizations, the 4th chapter expands the analysis of the influence of variables like Human Resource Management, Organizational Climate, Psychological Contract and KSA (Knowledge, Skills, Abilities) on the relation sustainability. A detailed analysis of these relations is provided and a research hypothesis are built. According to this new framework in 5th chapter a statistical analysis was performed to qualify and quantify the influence of Organizational Climate on the Relations Sustainability. To this end the Structural Equation Modeling (SEMs) has adopted as method for the definition of the latent variables and the measure of their relations. The results obtained are satisfactory. An effective strategy to motivate the respondents to participate in the survey seems to be at the moment one of the major obstacles to the analysis implementation since the organizational performances are not specifically required by the projects’ evaluation guidelines and they represent an increase in the project related transaction costs. Their explicit introduction in the project presentation guidelines should be explored as an opportunity to increase the chances of success of these projects.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Low Correlated Sequences & Architectures and Algorithms for Analog-to-Information Converters: Theory, Design, Implementation and Applications.

Most electronic systems can be described in a very simplified way as an assemblage of analog and digital components put all together in order to perform a certain function. Nowadays, there is an increasing tendency to reduce the analog components, and to replace them by operations performed in the digital domain. This tendency has led to the emergence of new electronic systems that are more flexible, cheaper and robust. However, no matter the amount of digital process implemented, there will be always an analog part to be sorted out and thus, the step of converting digital signals into analog signals and vice versa cannot be avoided. This conversion can be more or less complex depending on the characteristics of the signals. Thus, even if it is desirable to replace functions carried out by analog components by digital processes, it is equally important to do so in a way that simplifies the conversion from digital to analog signals and vice versa. In the present thesis, we have study strategies based on increasing the amount of processing in the digital domain in such a way that the implementation of analog hardware stages can be simplified. To this aim, we have proposed the use of very low quantized signals, i.e. 1-bit, for the acquisition and for the generation of particular classes of signals.

Coordination and Control of Autonomous Mobile Robots Swarms by using Particle Swarm Optimization Algorithm and Consensus Theory

This thesis presents some different techniques designed to drive a swarm of robots in an a-priori unknown environment in order to move the group from a starting area to a final one avoiding obstacles. The presented techniques are based on two different theories used alone or in combination: Swarm Intelligence (SI) and Graph Theory. Both theories are based on the study of interactions between different entities (also called agents or units) in Multi- Agent Systems (MAS). The first one belongs to the Artificial Intelligence context and the second one to the Distributed Systems context. These theories, each one from its own point of view, exploit the emergent behaviour that comes from the interactive work of the entities, in order to achieve a common goal. The features of flexibility and adaptability of the swarm have been exploited with the aim to overcome and to minimize difficulties and problems that can affect one or more units of the group, having minimal impact to the whole group and to the common main target. Another aim of this work is to show the importance of the information shared between the units of the group, such as the communication topology, because it helps to maintain the environmental information, detected by each single agent, updated among the swarm. Swarm Intelligence has been applied to the presented technique, through the Particle Swarm Optimization algorithm (PSO), taking advantage of its features as a navigation system. The Graph Theory has been applied by exploiting Consensus and the application of the agreement protocol with the aim to maintain the units in a desired and controlled formation. This approach has been followed in order to conserve the power of PSO and to control part of its random behaviour with a distributed control algorithm like Consensus.

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

New developments in state-specific multireference coupled-cluster theory

Coupled-cluster theory in its single-reference formulation represents one of the most successful approaches in quantum chemistry for the description of atoms and molecules. To extend the applicability of single-reference coupled-cluster theory to systems with degenerate or near-degenerate electronic configurations, multireference coupled-cluster methods have been suggested. One of the most promising formulations of multireference coupled cluster theory is the state-specific variant suggested by Mukherjee and co-workers (Mk-MRCC). Unlike other multireference coupled-cluster approaches, Mk-MRCC is a size-extensive theory and results obtained so far indicate that it has the potential to develop to a standard tool for high-accuracy quantum-chemical treatments. This work deals with developments to overcome the limitations in the applicability of the Mk-MRCC method. Therefore, an efficient Mk-MRCC algorithm has been implemented in the CFOUR program package to perform energy calculations within the singles and doubles (Mk-MRCCSD) and singles, doubles, and triples (Mk-MRCCSDT) approximations. This implementation exploits the special structure of the Mk-MRCC working equations that allows to adapt existing efficient single-reference coupled-cluster codes. The algorithm has the correct computational scaling of d*N^6 for Mk-MRCCSD and d*N^8 for Mk-MRCCSDT, where N denotes the system size and d the number of reference determinants. For the determination of molecular properties as the equilibrium geometry, the theory of analytic first derivatives of the energy for the Mk-MRCC method has been developed using a Lagrange formalism. The Mk-MRCC gradients within the CCSD and CCSDT approximation have been implemented and their applicability has been demonstrated for various compounds such as 2,6-pyridyne, the 2,6-pyridyne cation, m-benzyne, ozone and cyclobutadiene. The development of analytic gradients for Mk-MRCC offers the possibility of routinely locating minima and transition states on the potential energy surface. It can be considered as a key step towards routine investigation of multireference systems and calculation of their properties. As the full inclusion of triple excitations in Mk-MRCC energy calculations is computational demanding, a parallel implementation is presented in order to circumvent limitations due to the required execution time. The proposed scheme is based on the adaption of a highly efficient serial Mk-MRCCSDT code by parallelizing the time-determining steps. A first application to 2,6-pyridyne is presented to demonstrate the efficiency of the current implementation.