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

Capital Adequacy Ratios, Efficiency and Governance: a Comparison Between Islamic and Western Banks

The profit and loss sharing principle that is peculiar to Islamic finance reformulates the allocation of risk between stakeholders. Since in Islamic banks depositors are closer to stockholders in terms of residual claiming on profits, the relationship between capitalization and efficiency should in principle be weaker than in their Western counterparts. Results, obtained by means of a stochastic cost frontier analysis on samples of European-15 and Islamic banks during the period 1996-2002, show that the ratio of equity to deposits negatively affects inefficiency in both types of banks, but this effect is considerably undersized in Islamic banks as compared to European ones. This supports the reluctance that has accompained the proposal of capital adequacy ratios for Islamic banks in accordance to Basel Agreements.Islamic Banks, capital, governance.

SMD-based numerical stochastic perturbation theory

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schr\"odinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.Comment: 35 pages, 4 figures; v2: corrected typos, coincides with published versio

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.

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