The partition function of an interacting many body system: beyond the perturbed static path approximation

Based on the path integral representation of the partition function of a many body system with separable two body interaction we propose a systematic extension of the perturbed static path approximation (PSPA) to lower temperatures. Thereby, special attention must be paid to instabilities of the classical mean field solution in functional space that cause divergencies within the conventional PSPA. As a result we develop an approximation applicable from high to very low temperatures. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin model. In particular, we obtain a very good approximation to the level density of the Lipkin model even at low thermal excitations. Our results may have potential applications in low temperature nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. PACS: 5.30.-d, 24.60.-k, 21.10.Ma, 74.25.BtComment: 11 pages, 7 figures, replaced with shortened version accepted for publication in EPJB, minor changes not affecting any result

Age and gender composition of the workforce, productivity and profits: Evidence from a new type of data for German enterprises

This empirical paper documents the relationship between composition of a firm's workforce (with a special focus on age and gender) and its performance (productivity and profitability) for a large representative sample of enterprises from manufacturing industries in Germany. We use unique newly available data that for the first time combine information from the statistics of employees covered by social security that is aggregated at the enterprise level and information from enterprise level surveys performed by the Statistical Offices. Our microeconometric analysis confirms previous findings of concave age-productivity profiles, which are consistent with human capital theory, and adds a new finding of a rather negative effect of age on firms' profitability, which is consistent with deferred compensation considerations. Moreover, our analysis reveals for the first time that the ceteris paribus lower level of productivity in firms with a higher share of female employees does not go hand in hand with a lower level of profitability in these firms. If anything, profitability is (slightly) higher in firms with a larger share of female employees. This finding might indicate that lower productivity of women is (over)compensated by lower wage costs for women, which might be driven by general labor market discrimination against women.Ageing, firm performance, gender, productivity, profitability, Germany

Survey Evidence on Conditional Norm Enforcement

We discuss survey evidence on individuals' willingness to sanction norm violations – such as evading taxes, drunk driving, fare dodging, or skiving off work – by expressing disapproval or social exclusion. Our data suggest that people condition their sanctioning behavior on their belief about the frequency of norm violations. The more commonly a norm violation is believed to occur, the lower the individuals' inclination to punish it. Based on an instrumental variable approach, we demonstrate that this pattern reflects a causal relationship.Norm Enforcement, Sanctioning, Social Norms, Survey Evidence

Survey Evidence on Conditional Norm Enforcement

We discuss survey evidence on individuals' willingness to sanction norm violations - such as evading taxes, drunk driving, fare dodging, or skiving o work - by expressing disapproval or social exclusion. Our data suggest that people condition their sanctioning behavior on their belief about the frequency of norm violations. The more commonly a norm violation is believed to occur, the lower the individuals' inclination to punish it. Based on an instrumental variable approach, we demonstrate that this pattern reflects a causal relationship.Norm Enforcement; Sanctioning; Social Norms; Survey Evidence

Differential K-theory. A survey

Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in mathematical physics. In this survey, we describe the developments of the recent decades in this area. In particular, we discuss axiomatic characterizations of differential K-theory (and that these uniquely characterize differential K-theory). We describe several explicit constructions, based on vector bundles, on families of differential operators, or using homotopy theory and classifying spaces. We explain the most important properties, in particular about the multiplicative structure and push-forward maps and will state versions of the Riemann-Roch theorem and of Atiyah-Singer family index theorem for differential K-theory.Comment: 50 pages, report based in particular on work done sponsored the DFG SSP "Globale Differentialgeometrie". v2: final version (only typos corrected), to appear in C. B\"ar et al. (eds.), Global Differential Geometry, Springer Proceedings in Mathematics 17, Springer-Verlag Berlin Heidelberg 201

Brain rhythms of pain

Pain is an integrative phenomenon that results from dynamic interactions between sensory and contextual (i.e., cognitive, emotional, and motivational) processes. In the brain the experience of pain is associated with neuronal oscillations and synchrony at different frequencies. However, an overarching framework for the significance of oscillations for pain remains lacking. Recent concepts relate oscillations at different frequencies to the routing of information flow in the brain and the signaling of predictions and prediction errors. The application of these concepts to pain promises insights into how flexible routing of information flow coordinates diverse processes that merge into the experience of pain. Such insights might have implications for the understanding and treatment of chronic pain

Compact quantum metric spaces from quantum groups of rapid decay

We present a modified version of the definition of property RD for discrete quantum groups given by Vergnioux in order to accommodate examples of non-unimodular quantum groups. Moreover we extend the construction of spectral triples associated to discrete groups with length functions, originally due to Connes, to the setting of quantum groups. For quantum groups of rapid decay we study the resulting spectral triples from the point of view of compact quantum metric spaces in the sense of Rieffel.Comment: 19 page

Parallel Quantum Circuit in a Tunnel Junction

The spectrum of 1-state and 2-states per line quantum buses is used to determine the effective $V_{ab}(N)$ electronic coupling between emitter and receiver states through the bus as a function of the number $N$ of parallel lines in the bus. When the calculation of $V_{ab}(N)$ is spectrally difficult, an Heisenberg-Rabi time dependent quantum exchange process can be triggered through the bus by preparing a specific initial non-stationanry state and identifying a target state to capture the effective oscillation frequency $\Omega_{ab}(N)$ between those. For $\Omega_{ab}(N)$ (for $V_{ab}(N)$), two different regimes are observed as a function of $N$: linear and $\sqrt{N}$ more moderate increases. This state preparation was remplaced by electronically coupling the quantum bus to two semi-infinite electrodes. The native quantum transduction process at work in this tunnel junction is not faithfully following the $\Omega_{ab}(N)$ variations with $N$. Due to normalisation to unity of the electronic transparency of the quantum bus and to the low pass filter character of the transduction, large $\Omega_{ab}(N)$ cannot be followed by the tunnel junction. At low coupling and when $N$ is small enough not to compensate the small through line coupling, an $N^2$ power law is preserved for $\Omega_{ab}(N)$. The limitations of the quantum transduction in a tunnel junction is pointing how the broadly used concept of electrical contact between a metallic nanopad and a molecular wire can be better described as a quantum transduction process

Learning Dictionaries with Bounded Self-Coherence

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables the sparse coding of signal observations with a small approximation error, while a low self-coherence of the atoms guarantees atom recovery and a more rapid residual error decay rate for the sparse coding algorithm. The two goals of high signal coherence and low self-coherence are typically in conflict, therefore one seeks a trade-off between them, depending on the application. We present a dictionary learning method with an effective control over the self-coherence of the trained dictionary, enabling a trade-off between maximizing the sparsity of codings and approximating an equiangular tight frame.Comment: 4 pages, 2 figures; IEEE Signal Processing Letters, vol. 19, no. 12, 201