The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics

This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical propagator of the classical Feynman path fluctuations. Pre-exponential factor approximations are necessary when chaotic or complex systems are simulated. We introduced pre-exponential factor approximations based either on analytical considerations or numerical regularization. The approximations are tested for power spectrum calculations of more and more chaotic model systems and on several molecules, for which exact quantum mechanical values are available. The results show that the pre-exponential factor approximations introduced are accurate enough to be safely employed for semiclassical simulations of complex systems

TFP convergence across European regions: a comparative spatial dynamics analysis

This paper proposes a fixed-effect panel methodology that enables us to simultaneously take into account both TFP and traditional neoclassical convergence. We analyse a sample of 199 regions in EU15 (plus Norway and Switzerland) between 1985 and 2006 and find the absence of an overall process of TFP convergence as we observe that TFP dispersion is virtually constant across the two sub-periods. This result is proved robust to the use of different estimation procedures such as simple LSDV, spatially corrected LSDV, Kiviet-corrected LSDV, and GMM à la Arellano and Bond. However, we also show that this absence of a strong process of global TFP convergence hides interesting dynamic patterns across regions. These patterns are revealed by the use of recent exploratory spatial data techniques that enable us to obtain a complete picture of the complex EU cross-regions dynamics. We find that, between 1985 and 2006, there has been numerous regional miracles and disasters in terms of TFP performance and that polarization patterns have significantly changed along time. Overall, results seem to suggest that a few TFP leaders are emerging and are distancing themselves from the rest, while the cluster of low TFP regions is increasing

Education and Italian Regional Development

Given recent emphasis on externality to education, macroeconomic studies have a role to play in the analysis of return to schooling. In this paper we study the connection between growth and human capital in a convergence regression for the panel of Italian regions. We include measures of average, primary, secondary and tertiary education. We find that increased education seems to contribute to growth only in the South. Decomposing total schooling into its three constituent parts, we find that only primary education in the South seems to be important. The results thus suggest that the Italian growth benefited from the elimination of illiteracy in the South, mainly in the 1960s, but not from the substantial increases in education at the other levels.Returns to education, regional Italian growth

"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra

Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems

A new semiclassical "divide-and-conquer" method is presented with the aim of demonstrating that quantum dynamics simulations of high dimensional molecular systems are doable. The method is first tested by calculating the quantum vibrational power spectra of water, methane, and benzene - three molecules of increasing dimensionality for which benchmark quantum results are available - and then applied to C60, a system characterized by 174 vibrational degrees of freedom. Results show that the approach can accurately account for quantum anharmonicities, purely quantum features like overtones, and the removal of degeneracy when the molecular symmetry is broken

A panel technique for the analysis of technology convergence: The case of the Italian regions

Differences in productivity levels represent a major component of the large cross-country differences in per capita income observed in international datasets and even in some regional ones. Nowadays, few economists would dispute neither this finding, nor that differences in productivity reflects – among other things – differences in technology levels. More controversial is the question of whether such differences in technology are stationary or temporary – that is, whether technology convergence is taking place, at what speed, under what conditions. This state of affairs is the result of several different difficulties faced by the empirical analysis on cross-country differences in per capita income growth rates. Recently, things have improved on both the analytical and the empirical side. On the analytical side, simple models in which technology convergence and capital-deepening can be studied within a common framework are now available. In these models the transitional dynamics is simple enough to be useful for empirical analysis [for instance, De la Fuente (1996) and (1997)]. On the empirical side, Islam (1995) has shown that we can test for the presence of technology heterogeneity in cross-country convergence analysis by using an appropriate fixed-effect panel estimator. The contribution of the present paper is on the empirical side. We propose a method designed to test whether part of the observed economic convergence is due to technology convergence. The method is based on the contribution by Islam (1995), but it extends it as follows. Islam’s technique was originally designed – and is currently applied – to measure cross-country differences in technology levels, assuming that such (relative) differences are at their stationary values and therefore that no technology convergence is present. The extension proposed in this paper builds on the a standard implication of models of technology convergence. If such convergence is present, the cross-sectional variance of the logs of our measure of technology should decreases over time approaching its stationary value. Alternatively, if technology convergence is absent, the variance is at its stationary value and no significant time-trend should be detected in its value. We exploit this difference to test for the presence of technology convergence in the data. First, we estimate the convergence equation over several sub-periods and use the values of the individual intercepts to compute the TFP levels. Then, we obtain the cross-section variance of the logs of our measures of TFP for each sub-period, and check whether the observed pattern is consistent either with catching-up hypothesis or with the hypothesis that the current degree of technology heterogeneity is at its stationary value. In this paper we use a panel dataset of the Italian regions, 1960-95. We apply our proposed methodology to the Italian case because it is notoriously characterized by a remarkable degree of regional heterogeneity. In spite of being one of the best known cases of regional divide, no explicit analysis of technology convergence across Italian regions is available yet. We use dynamic panel techniques (LSDV and GMM) to estimates our growth regressions. We split the whole sample period in several sub-periods to check for the presence of technology convergence. Our preliminary results reveal a significant presence of technology convergence, which reached its peak between the first and the second sub-period, and stayed significant but at a slower pace in later sub-periods. The emerging picture points to the simultaneous presence of technology convergence in a context otherwise characterized by weak output per-worker convergence. This is consistent with some recent results based on international datasets (e.g. Dowrick and Rogers [OEP (2002]).