Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio

The gradient flow coupling from numerical stochastic perturbation theory

Perturbative calculations of gradient flow observables are technically challenging. Current results are limited to a few quantities and, in general, to low perturbative orders. Numerical stochastic perturbation theory is a potentially powerful tool that may be applied in this context. Precise results using these techniques, however, require control over both statistical and systematic uncertainties. In this contribution, we discuss some recent algorithmic developments that lead to a substantial reduction of the cost of the computations. The matching of the ${\overline{\rm MS}}$ coupling with the gradient flow coupling in a finite box with Schr\"odinger functional boundary conditions is considered for illustration.Comment: Talk given at the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK; LaTeX source, 7 pages, 2 figure

Social mobility and fertility

Intra- and inter-generational social mobility have in the past played an important role in attempts to explain fertility behaviour, and continue to do so today. The opinions expressed by social scientists in the first part of the 20th century are renewed and confirmed. More specifically: (1) intra-generational social mobility has been reinforced by the personal well-being aspirations and job careers of women; (2) status anxiety parents feel for their children pushes fertility down in large areas of the developed world (mainly in southern European and eastern Asian countries). Therefore, the provocative idea of Ariès that in the rich world, the child-king has now been replaced by the couple-queen does not perfectly hold.demographic transition, fertility, social mobility

Study to regenerate the degraded neighborhood of San Carlo on the northern outskirt of Padua, Italy

The San Carlo neighborhood with the church of San Carlo at its center is a degraded area in the northern outskirts of Padua, a city located near Venice in the Veneto region of north-eastern Italy. Once marked by a distinctive identity, this part of the outskirts of Padua has gradually lost its social and functional character. The idea of restoring this decaying district has long been the subject of discussion by the local authorities. The neighborhood of San Carlo is one of the subjects recently investigated by students studying the \u2018Architectural and Urban Composition 2' course on the Master\u2019s Degree in Architectural Engineering at the University of Padua. Their ideas include a green piazza park, a community center and hall, a library, study rooms for students, additional parking, open space for the weekly market

Courts Delays and Crime Deterrence (An Application to Crimes Against Property in Italy)

Using Italian data in the period 1999-2002, we estimate the impact of trials delay on the willingness to commit crimes against property. However, the endogenous relationship that links the former to the latter could generate serious problems of inconsistency in the estimation procedure. Since geographical distance can be considered an exogenous determinant of the probability of belonging to peripheral courts, which are typically considered less efficient than main ones, it should represent a valid candidate instrument for trials delay. Estimates obtained by means of Two- Stages Least Squares show a significant positive effect of trials duration on crimes, supporting the hypothesis that some criminals are either sensitive to the discounting process of punishment or aware of the probability of prescription, or both. As a side result, we also find a relationship between courts' fragmentation and trials duration. This suggests that an optimal dimension of courts is likely to exist, and that policy makers should take this into consideration in the design of the jurisdictional geography.Illegal Behavior, enforcement of Law, Criminal Law.

An existence result for a nonlinear transmission problems

Let $\Omega^o$ and $\Omega^i$ be open bounded subsets of $\mathbb{R}^n$ of class $C^{1,\alpha}$ such that the closure of $\Omega^i$ is contained in $\Omega^o$. Let $f^o$ be a function in $C^{1,\alpha}(\partial\Omega^o)$ and let $F$ and $G$ be continuous functions from $\partial\Omega^i\times\mathbb{R}$ to $\mathbb{R}$. By exploiting an argument based on potential theory and on the Leray-Schauder principle we show that under suitable and completely explicit conditions on $F$ and $G$ there exists at least one pair of continuous functions $(u^o, u^i)$ such that $$\left\{ \begin{array}{ll} \Delta u^o=0&\text{in }\Omega^o\setminus\mathrm{cl}\Omega^i\,,\\ \Delta u^i=0&\text{in }\Omega^i\,,\\ u^o(x)=f^o(x)&\text{for all }x\in\partial\Omega^o\,,\\ u^o(x)=F(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,,\\ \nu_{\Omega^i}\cdot\nabla u^o(x)-\nu_{\Omega^i}\cdot\nabla u^i(x)=G(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,, \end{array} \right.$$ where the last equality is attained in certain weak sense. In a simple example we show that such a pair of functions $(u^o, u^i)$ is in general neither unique nor local unique. If instead the fourth condition of the problem is obtained by a small nonlinear perturbation of a homogeneous linear condition, then we can prove the existence of at least one classical solution which is in addition locally unique