On Quantum Groups in the Hubbard Model with Phonons

The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum symmetry only for D = 1 and that terms of higher order in the fermionic operators in addition to phonons are required for a quantum symmetric hamiltonian. The condition for quantum symmetry is "half filling" and there is no local electron-phonon coupling. A discussion of Quantum symmetries in general is given in a formalism that should be readily accessible to non Hopf-algebraists.Comment: latex, 17 page

Covariant differential complexes on quantum linear groups

We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all monomials of these forms possess the unique ordering. For the obtained external algebras we define the exterior derivative possessing the usual nilpotence condition, and the generally deformed version of Leibniz rules. The status of the known examples of GL_q(N)-differential calculi in the proposed classification scheme, and the problems of SL_q(N)-reduction are discussed.Comment: 23 page

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.Comment: 38 pages, no figure

Developing SOEPsurvey and SOEPservice: The (Near) Future of the German Socio-Economic Panel Study (SOEP)

Das Sozio-oekonomische Panel (SOEP) ist als multidisziplinäres Haushaltspanel, das Informationen zu allen Personen, die in einem Panel-Haushalt leben, erhebt und damit alle Altersjahrgänge abdeckt, nach 25 Jahren Laufzeit auch zu einer Kohorten- Studie geworden. Der zunehmende Erfolg der Forschungsinfrastruktur-Einrichtung SOEP speist sich in erster Linie daraus, dass die Analysekraft von Längsschnittstudien mit jedem weiteren Erhebungsjahr zunimmt. Hinzu kommen im Falle des SOEP seit Beginn an eine lange Reihe von Innovationen bei der Erhebung, Datenaufbereitung und Nutzer-Service. Deswegen gilt es zu überlegen, wie die wissenschaftliche Power des SOEP weiter gestärkt werden kann. Nicht zuletzt auch, da es für neue, spezialisierte Panel-Studien (wie das Nationale Bildungspanel oder das DFG-geförderte Familienpanel PAIRFAM) eine Referenz und ggf. Verankerung der Hochrechnung darstellt. Zudem kann das SOEP künftig eine größere Rolle als ,,Kontroll-Stichprobe" für Interventions-Studien spielen; etwa im Bereich der Kindheitsentwicklung. Auf diese neuen Rollen muss es vorbereitet sein. Die im SOEP in den letzten Jahren realisierten Erhebungsinnovationen wie z. B. die Inkorporation psychologischer Konzepte, physische Gesundheitsmessungen (Greifkraft), die Messung kognitiver Fähigkeiten und die Erprobung von Verhaltens- Experimenten werden in anderen Panel-Studien aufgegriffen und auf eine größere Stichprobenbasis gestellt. Im UK wird mit ,,Understanding Society" ein Haushaltspanel mit 40.000 Haushalten begonnen; in den Niederlanden wird mit MESS ein Haushaltspanel von über 5.000 Haushalten für innovative Messmethoden zur Verfügung gestellt. Die Erhebungsinhalte des SOEP werden von den Forschungs- und Politikberatungs-Communities unverändert stark nachgefragt. In UK hat ein für ,,Understanding Society" breit angelegter Konsultationsprozess keine grundsätzlich neuen Befragungsinhalte zu Tage gefördert, die das SOEP nicht bereits enthält oder die für das SOEP ohnehin im Gespräch sind. Wichtiger als die ,,Entdeckung" völlig neuer Erhebungsinhalte ist das thematische wie zeitliche ,,Zuschneiden" der Details von Befragungsinhalten auf (zugespitzte) neue (theoretische) Fragestellungen und dabei gleichzeitig bewährte sowie viel genutzte zentrale Befragungsinhalte und deren Befragungsrhythmen beizubehalten. Das ,,Maßschneidern" von Erhebungsinhalten wird in den nächsten Jahren die eigentliche Herausforderung für Infrastruktur- Erhebungen wie die PSID, ,,Understanding Society" und das SOEP sein. Bei den Erhebungsinhalten sollten die ,,Ränder" des Lebenslaufs eine größere Rolle spielen, da diese von Haushalts-Panels besonders gut erfasst werden können. Diese Verbesserungen der Erhebungen beziehen sich einerseits auf die fötale Phase von in das SOEP hineingeborenen Kindern und die (frühe) Kindheit, andererseits auf die letzte Lebensphase und das Sterben. In der Mitte des Lebenslaufs werden verbesserte Fragen zum Einkommen, Sparen und Vermögen sowie auch psychologische Konstrukte eine zentrale Rolle spielen, außerdem gezielte Fragen (event triggered questionnaires) in Verbindung mit zentralen Lebensereignissen wie z. B. Eheschließung, Scheidung, Eintritt in und Austritt aus Arbeitslosigkeit. Es wird die Etablierung einer SOEP-"Innovations-Stichprobe" vorbereitet, um theoriegeleitete Forschungsfragen gezielter unterstützen zu können. Dazu wird es auch notwendig sein, neue Messkonzepte zu erproben (z. B. die Erhebung von Biomarkern, qualitative Erhebungen, aber auch Experimente und gezielte Interventionsstudien). Um die Power von Längsschnittdaten von Anfang an für die Innovations-Stichprobe ausnutzen zu können, ist geplant, zwei kleinere Teilstichproben des SOEP, die seit 1998 bzw. 2006 laufen (Subsamples E und H), in die Innovationsstichprobe zu überführen. Um die statistische Power langlaufender Längsschnittdaten entscheidend zu verbessern, schätzen wir eine Mindestfallzahl von etwa 500 Personen pro Geburtsund Alterskohorte für ausreichend ein. Um dieses Ziel zu erreichen, muss die Fallzahl des SOEP-Standard-Samples erhöht werden. Als ,,Nebeneffekt" werden dadurch wesentlich bessere Analysen für relativ kleine Gruppen in der Bevölkerung möglich; etwa für allein Erziehende oder bestimme Immigrantengruppen. Außerdem verbessern sich als weiterer ,,Nebeneffekt" auch regionale Analysemöglichkeiten, z. B. für die meisten Bundesländer und in großen Bundesländern bis hin zu Regierungsbezirken (oder ähnlich abgegrenzten regionalen Einheiten). In letzter Zeit wird immer deutlicher, welche große Bedeutung das SOEP als ,,Referenz-Datensatz" für spezialisierte und vom SOEP völlig unabhängige Erhebungen hat (neben Beobachtungsstudien, wie etwa Zwillings-Studien, auch Labor- und Interventions-Studien). Zur Unterstützung dieser Funktion ist eine neue Art von Service, der in Deutschland bislang nicht vorgehalten wird, notwendig (Beratung von Spezial-Erhebungen; ggf. Datenaufbereitung von längsschnittlichen Spezial-Erhebungen), der auch in ein Datenservicezentrum eingebracht werden könnte. After 25 years as a multidisciplinary household panel containing information on all individuals residing in panel households and thus covering all age cohorts, the German Socio-Economic Panel (SOEP) has become a true cohort study as well. The increasing success of the SOEP research infrastructure comes above all from the increasing analytical power that longitudinal studies attain with each successive survey year. In the case of SOEP, a long series of innovations in surveying, data preparation, and user service have also played a major role. For this reason, it is important to consider how the scientific capacity of SOEP can be further enhanced-- not least of all since the SOEP can form a key point of reference (or "anchor") for new, specialized panel studies (such as the National Educational Panel and the family panel PAIRFAM, funded by the German Research Foundation). Furthermore SOEP can become a kind of "control sample" for intervention studies, for example, in the field of child development. The SOEP survey and its governance structures must be prepared for these new tasks. The numerous innovations introduced into SOEP in recent years--questions dealing with psychological concepts, physical health measures (grip strength), measures of cognitive capabilities, and behavioral experiments--have been incorporated into other panel studies as well, and thus provided with a larger sample base. In the UK, the "Understanding Society" household panel study was launched with 40,000 households; in the Netherlands, the MESS household panel study of over 5,000 households offered a new basis for testing innovative measurement methods. The results of the SOEP survey are in continuing high demand in the research and policy advisory community. From our point of view, the large-scale consultation process conducted to define the content of the UK survey "Understanding Society" failed to identify any fundamentally new survey content that the SOEP either did not already contain or that was not already being discussed for the SOEP. More important than "discovering" entirely new survey areas is "tailoring" the details of existing survey content to address new, more specific (theoretical) questions, and thus maintaining proven and widely used elements of survey content. The "tailoring" of survey content will be the real challenge facing infrastructure surveys like PSID, "Understanding Society," and the SOEP in the coming years. In the future, the "margins" of the life course should play a stronger role in survey content, since household panels are able to provide outstanding data of these life phases. The SOEP, and other household panel surveys, can be improved, on the one hand, by including the fetal phase of life and early childhood for children born into the panel, and on the other, by including late life and death. In the middle of the life course, improved questions on income, savings, and wealth as well as psychological constructs will play a central role, as will specific questions (in "eventtriggered" questionnaires) on central life occurrences such as marriage, divorce, and entry into and exit from unemployment. Current plans for SOEP foresee the addition of an "Innovation Sample" that will make it possible to better address theory-based research questions required for testing new measurement concepts (e.g., the surveying of biomarkers, qualitative surveys, but also experiments and targeted intervention studies). In order to exploit the power of longitudinal data from the outset, we plan to incorporate two smaller SOEP subsamples that have been running since 1998 and 2006 (Subsamples E and H, respectively) into the Innovation Sample. In order to decisively improve the statistical power of long-term longitudinal data, we believe that a minimum case number of about 500 persons per birth and age cohort is required. In order to reach this goal, the case number in the SOEP standard samples needs to be increased. A positive side-effect of this enlargement would be a significantly improved potential for analyses of relatively small groups within the population: for example, lone parents or specific immigrant groups. Another positive side-effect would be an improved potential for regional analyses: for example, for the majority of federal states. In recent times, the importance of SOEP as a "reference dataset" for specialized surveys which are independent from SOEP (observational studies such as twin studies, and laboratory and intervention studies) has become strikingly evident. To enhance this important function, new types of service are needed (advice on special surveys, possibly also data preparation for special surveys), which could become part of a Data Service Center.Household Panels, German Socio-Economic Panel Study, SOEP

Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix \theta^{\mu\nu} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain --for N>=3, the case with N=2 being trivial-- the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.Comment: 33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3: New types of field redefinitions were considered, which make the large N U(N) and the SU(N) theories renormalisable. The conclusions for U(N) with finite N remain unchanged. Version 4: Corrected mistyped equations, minor revision

On the Differential Geometry of GLq(1∣1)GL_q(1| 1)

The differential calculus on the quantum supergroup GL$_q(1| 1)$ was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GL$_q(1| 1)$ in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix $\hat{R}$Comment: 14 page

Explicit attention interferes with selective emotion processing in human extrastriate cortex

BACKGROUND: Brain imaging and event-related potential studies provide strong evidence that emotional stimuli guide selective attention in visual processing. A reflection of the emotional attention capture is the increased Early Posterior Negativity (EPN) for pleasant and unpleasant compared to neutral images (~150–300 ms poststimulus). The present study explored whether this early emotion discrimination reflects an automatic phenomenon or is subject to interference by competing processing demands. Thus, emotional processing was assessed while participants performed a concurrent feature-based attention task varying in processing demands. RESULTS: Participants successfully performed the primary visual attention task as revealed by behavioral performance and selected event-related potential components (Selection Negativity and P3b). Replicating previous results, emotional modulation of the EPN was observed in a task condition with low processing demands. In contrast, pleasant and unpleasant pictures failed to elicit increased EPN amplitudes compared to neutral images in more difficult explicit attention task conditions. Further analyses determined that even the processing of pleasant and unpleasant pictures high in emotional arousal is subject to interference in experimental conditions with high task demand. Taken together, performing demanding feature-based counting tasks interfered with differential emotion processing indexed by the EPN. CONCLUSION: The present findings demonstrate that taxing processing resources by a competing primary visual attention task markedly attenuated the early discrimination of emotional from neutral picture contents. Thus, these results provide further empirical support for an interference account of the emotion-attention interaction under conditions of competition. Previous studies revealed the interference of selective emotion processing when attentional resources were directed to locations of explicitly task-relevant stimuli. The present data suggest that interference of emotion processing by competing task demands is a more general phenomenon extending to the domain of feature-based attention. Furthermore, the results are inconsistent with the notion of effortlessness, i.e., early emotion discrimination despite concurrent task demands. These findings implicate to assess the presumed automatic nature of emotion processing at the level of specific aspects rather than considering automaticity as an all-or-none phenomenon

Bicovariant Differential Geometry of the Quantum Group SLh(2)SL_h(2)

There are only two quantum group structures on the space of two by two unimodular matrices, these are the $SL_q(2)$ and the $SL_h(2)$ [9-13] quantum groups. One can not construct a differential geometry on $SL_q(2)$, which at the same time is bicovariant, has three generators, and satisfies the Liebnitz rule. We show that such a differential geometry exists for the quantum group $SL_h(2)$ and derive all of its properties

Diffraction efficiency of localized holograms in doubly doped LiNbo(3) crystals

The diffraction efficiency of M holograms superimposed in the volume of the recording medium is proportional to 1/M-2, me present a method, based on nondestructive localized holograms in a doubly doped LiNbO3 crystal, that allows us to also record M holograms in the same volume without an exposure schedule or a diffraction efficiency that has 1/M dependence. We compare experimentally the final diffraction efficiency obtained with the localized and distributed recording methods. (C) 2000 Optical Society of America OCIS codes: 090.0090, 210.0210

Nominal or Real? The Impact of Regional Price Levels on Satisfaction with Life

According to economic theory, real income, i.e., nominal income adjusted for purchasing power, should be the relevant source of life satisfaction. Previous work, however, has only studied the impact of inflation adjusted nominal income and not taken into account regional differences in purchasing power. Therefore, we use a novel data set to study how regional price levels affect satisfaction with life. The data set comprises about 7 million data points that are used to construct a price level for each of the 428 administrative districts in Germany. We estimate pooled OLS and ordered probit models that include a comprehensive set of individual level, time-varying and time-invariant control variables as well as control variables that capture district heterogeneity other than the price level. Our results show that higher price levels significantly reduce life satisfaction. Furthermore, we find that a higher price level tends to induce a larger loss in life satisfaction than a corresponding decrease in nominal income. A formal test of neutrality of money, however, does not reject neutrality of money. Our results provide an argument in favor of regional indexation of government transfer payments such as social welfare benefits