One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM functional theory. To avoid non-uniqueness issues we consider the case of fermionic and bosonic systems at elevated temperature and variable particle number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space is finite-dimensional due to the Pauli principle and we can provide a rigorous 1RDM functional theory relatively straightforwardly. For the bosonic case, where arbitrarily many particles can occupy a single state, the Fock space is infinite-dimensional and mathematical subtleties (not every hermitian Hamiltonian is self-adjoint, expectation values can become infinite, and not every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose restrictions on the allowed Hamiltonians and external non-local potentials. For simple conditions on the interaction of the bosons a rigorous 1RDM functional theory can be established, where we exploit the fact that due to the finite one-particle space all 1RDMs are finite-dimensional. We also discuss the problems arising from 1RDM functional theory as well as DFT formulated for an infinite-dimensional one-particle space.Comment: 55 pages, 7 figure

Modellierung ökonomischer Kompetenz in einer Pilotstudie zu ECOS

Die Modellierung ökonomische Kompetenz zur empirischen Erfassung einer Economic Literacy gehört immer noch zu den Forschungsdesideraten innerhalb der Ökonomischen Bildung.Bisher gelang es nicht, ein überzeugendes Modell für die empirische Erfassung vorzulegen,das den Ansprüchen einer deutschlandweiten Testung genügt. Dies verdeutlicht der nachfolgende Beitrag, indem er in einem Dreischritt, ausgehend von einer detaillierten Synthese der Kompetenzdefinition von Weinert, die bisherigen Studien aus dem Bereich der ökonomischen Bildung einer kritischen Anforderungsanalyse unterzieht, um anschließend zu versuchen, die bestehenden Ansätze in ein neues Modell für die Modellierung ökonomischer Kompetenz zu integrieren. Dieses Konstrukt zielt auf die Behebung der identifizierten Problemlagen und somit auf die Öffnung ökonomischer Kompetenz für empirische Tests. Es bildet die Basis für die Pilotstudie zu ECOS.Modelling Economic Literacy is still one of the research desiderata in economic education. Up to now, a convincing model for an empirical analysis was not yet presented that meets the requirements of a large-scale assessment. This is illustrated in the paper at hand, starting with a detailed synthesis of the competence definition of Weinert. After that the previous studies in the field of economic education are subject to a critical analysis. Then we try to integrate our new model of Economic Literacy into the existing approaches. This construct,which is expected to fix the identified problem areas, would therefore open economic Literacy for empirical tests, forms the basis for the pilot study of ECOS

Cosmic dimensions

Martin's Axiom for $\sigma$-centered partial orders implies that there is a cosmic space with non-coinciding dimensions.Comment: 2005-11-15: new version, largely rewritte

Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory

We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy--Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.Comment: 12 pages, 7 figure

Framework of Measuring Economic Competencies

How to model economic competencies with the objective of empirically testing them? This question has been discussed for many years now without a conclusive measurement model having been presented thus far. Taking an in-depth analysis of the definition of competency proposed by Weinert (2001) as a starting point, we will derive a framework for the necessary complexity of competency assessment, which finds its graphical representation in a competence octagon. After discussing existing empirical work in the field of economic education and classifying it using the categories of the competence octagon, we will then propose a new model of economic competency that allows for empirical testing

Let me Entertain You – the Influence of Augmented Reality on Purchasing Intention in E-Commerce

Augmented reality (AR) in e-commerce helps consumers to envision products in their respective surroundings, so fosters customer experience. Our online experiment with 302 probands explores the effect of AR on purchasing intention, taking into account motivational variables—perceived usefulness, entertainment and perceived ease of use (PEOU). Consumers viewing products in an AR-enabled online shop rated perceived usefulness, entertainment and PEOU significantly higher than the control group viewing the non-AR-enabled online shop. Performing mediation analysis, we found that AR significantly influences purchase intention, which is mediated by perceived entertainment. Our findings add to the understanding of the interplay of the motivational variables perceived usefulness, entertainment and PEOU as well as the impact of AR on customer decision making. From a managerial point of view, our findings suggest that in the current stage of the technology, AR is perceived as a playful add-on to online shopping, positively impacting purchase intention

The social side of brick and mortar: the impact of brand-related user-generated content on different consumer typologies in food retailing

Social media influences most off-line purchasing decisions, thereby impacting the relationship between retailers and (prospective) customers. User-generated content (UGC) is a means of engaging with consumers and shaping their trust perception and loyalty. Based on a sample of 967 food retail customers, we identify four segments into which brand-related UGC consumers can be categorized: Brand Lovers, True-Blues, Detached Customers, and Confiding Customers. These clusters are distinct in terms of trust toward brand-related UGC, loyalty, brand-related UGC involvement, and demographics. Our findings add to the understanding of digital content marketing consequences by mapping four different brand-related UGC consumer typologies. From a managerial point of view, our findings suggest how to best engage with the determined consumer typologies and highlight the importance of social media for off-line businesses

Experimental investigation of the turbulent Schmidt number in supersonic film cooling with shock interaction

The interaction of an impinging shock and a supersonic helium cooling film is investigated experimentally by high-speed particle-image velocimetry. A laminar helium jet is tangentially injected into a turbulent air freestream at a freestream Mach number $Ma_\infty=2.45$. The helium cooling film is injected at a Mach number $Ma_i=1.30$ at a total temperature ratio $T_{0,i}/T_{0,\infty}=0.75$. A deflection $\beta=8\deg$ generates a shock that impinges upon the cooling film. A shock interaction case and a reference case without shock interaction are considered. The helium mass fraction fluctuations are measured and the turbulent mass flux as well as the turbulent Schmidt number are determined qualitatively. For comparison, large-eddy simulation (LES) results of a comparable flow configuration are used. The streamwise and wall-normal turbulent mass fluxes are in qualitative agreement with the LES data. The turbulent Schmidt number differs significantly from unity. Without shock interaction, the turbulent Schmidt number is in the range $0.5 \leq Sc_t \leq 1.5$ which is in agreement with the literature. With shock interaction, the turbulent Schmidt number varies drastically in the vicinity of the shock interaction. Thus, the experimental results confirm the numerical data showing a massively varying turbulent Schmidt number in supersonic film cooling flows, i.e., the standard assumption of a constant turbulent Schmidt number is valid neither without nor with shock interaction

Informal learning and economic education

Ein Großteil ökonomischer Kompetenzen bei Jugendlichen wird vermutlich informell gelernt, da ökonomische Bildung in Deutschland nur zu einem geringen Umfang im Unterricht gelehrt wird. Zur Diagnose von Art und Umfang informellen Lernens im Bereich der ökonomischen Bildung erläutern die Autoren die theoretischen Hintergründe und stellen ein Pilotprojekt zur Kompetenzmessung in der ökonomischen Bildung vor (ECOS - Economic Competencies Study). In diesem Projekt wird die Performanz in einer simulierten Online-Umgebung als Indikator für Kompetenzen angesehen. Mit diesem Verfahren sollen informell erworbene Kompetenzen quantitativ erfasst werden.The authors argue that a large part of economic competencies in adolescents are likely to be acquired in informal settings because generally economic education is taught only to a small amount in German schools. In order to assess the very character and extend of in-formal learning in economic education the authors explain the theoretic background and present a pilot project (ECOS - Economic Competencies Study). We assume that performance in a simulated online environment is regarded as an indicator for competencies. With this method informally acquired competencies in economic education are to be quantitatively assessed