Normalization of the chiral condensate in the massive Schwinger model

Within mass perturbation theory, already the first order contribution to the chiral condensate of the massive Schwinger model is UV divergent. We discuss the problem of choosing a proper normalization and, by making use of some bosonization results, we are able to choose a normalization so that the resulting chiral condensate may be compared, e.g., with lattice data.Comment: Latex file, 8 pages, 1 figure, needed macro: psbox.te

Quantum correlations and thermodynamic performances of two-qubit engines with local and collective baths

We investigate heat engines whose working substance is made of two coupled qubits performing a generalised Otto cycle by varying their applied magnetic field or their interaction strength during the compression and expansion strokes. During the heating and cooling strokes, the two qubits are coupled to local and common environments that are not necessarily at equilibrium. We find instances of quantum engines coupled to non equilibrium common environments exhibiting non-trivial connections to quantum correlations as witnessed by a monotonic dependence of the work produced on quantum discord and entanglement.Comment: Close to published versio

What Regulates Galaxy Evolution? Open Questions in Our Understanding of Galaxy Formation and Evolution

In April 2013, a workshop entitled "What Regulates Galaxy Evolution" was held at the Lorentz Center. The aim of the workshop was to bring together the observational and theoretical community working on galaxy evolution, and to discuss in depth of the current problems in the subject, as well as to review the most recent observational constraints. A total of 42 astrophysicists attended the workshop. A significant fraction of the time was devoted to identifying the most interesting "open questions" in the field, and to discuss how progress can be made. This review discusses the four questions (one for each day of the workshop) that, in our opinion, were the focus of the most intense debate. We present each question in its context, and close with a discussion of what future directions should be pursued in order to make progress on these problems.Comment: 36 pages, 6 Figures, submitted to New Astronomy Review

Bisector energy and few distinct distances

We introduce the bisector energy of an $n$-point set $P$ in $\mathbb{R}^2$, defined as the number of quadruples $(a,b,c,d)$ from $P$ such that $a$ and $b$ determine the same perpendicular bisector as $c$ and $d$. If no line or circle contains $M(n)$ points of $P$, then we prove that the bisector energy is $O(M(n)^{\frac{2}{5}}n^{\frac{12}{5}+\epsilon} + M(n)n^2).$. We also prove the lower bound $\Omega(M(n)n^2)$, which matches our upper bound when $M(n)$ is large. We use our upper bound on the bisector energy to obtain two rather different results: (i) If $P$ determines $O(n/\sqrt{\log n})$ distinct distances, then for any $0<\alpha\le 1/4$, either there exists a line or circle that contains $n^\alpha$ points of $P$, or there exist $\Omega(n^{8/5-12\alpha/5-\epsilon})$ distinct lines that contain $\Omega(\sqrt{\log n})$ points of $P$. This result provides new information on a conjecture of Erd\H{o}s regarding the structure of point sets with few distinct distances. (ii) If no line or circle contains $M(n)$ points of $P$, then the number of distinct perpendicular bisectors determined by $P$ is $\Omega(\min\{M(n)^{-2/5}n^{8/5-\epsilon}, M(n)^{-1} n^2\})$. This appears to be the first higher-dimensional example in a framework for studying the expansion properties of polynomials and rational functions over $\mathbb{R}$, initiated by Elekes and R\'onyai.Comment: 18 pages, 2 figure

Asymmetric Monetary Transmission in EMU: The Robustness of VAR Conclusions and Cecchetti’s Legal Family Theory

We review studies on monetary transmission in the EU countries using the VAR approach and analyse why they often lead to divergent outcomes. Firstly, we estimate 43 VAR models across ten EU countries and compare the robustness of the ranking of the magnitudes of the price and output responses. The main specification differences between the VAR models are the use of two different sample periods; the inclusion of additional variables; and the use of recursive, long run, and structural identification schemes. Secondly, we calculate rank correlations between the output and price responses of a recursive VAR and a structural VAR to the financial structure indicators used by Cecchetti (1999), who argued that legal systems cause financial structure, which in turn causes asymmetric transmission. In contrast to Cecchetti, we find that there is little correlation.monetary transmission, VAR models, EMU

Barriers to Transport and Mixing in Volume-Preserving Maps with Nonzero Flux

In this paper we identify the geometric structures that restrict transport and mixing in perturbations of integrable volume-preserving systems with nonzero net flux. Unlike KAM tori, these objects cannot be continued to the tori present in the integrable system but are generated by resonance and have a contractible direction. We introduce a remarkably simple algorithm to analyze the behavior of these maps and obtain quantitative properties of the tori. In particular, we present assertions regarding the distribution of the escape times of the unbounded orbits, the abundance of tori, and the size of the resonant regions