From the area under the Bessel excursion to anomalous diffusion of cold atoms

Levy flights are random walks in which the probability distribution of the step sizes is fat-tailed. Levy spatial diffusion has been observed for a collection of ultra-cold Rb atoms and single Mg+ ions in an optical lattice. Using the semiclassical theory of Sisyphus cooling, we treat the problem as a coupled Levy walk, with correlations between the length and duration of the excursions. The problem is related to the area under Bessel excursions, overdamped Langevin motions that start and end at the origin, constrained to remain positive, in the presence of an external logarithmic potential. In the limit of a weak potential, the Airy distribution describing the areal distribution of the Brownian excursion is found. Three distinct phases of the dynamics are studied: normal diffusion, Levy diffusion and, below a certain critical depth of the optical potential, x~ t^{3/2} scaling. The focus of the paper is the analytical calculation of the joint probability density function from a newly developed theory of the area under the Bessel excursion. The latter describes the spatiotemporal correlations in the problem and is the microscopic input needed to characterize the spatial diffusion of the atomic cloud. A modified Montroll-Weiss (MW) equation for the density is obtained, which depends on the statistics of velocity excursions and meanders. The meander, a random walk in velocity space which starts at the origin and does not cross it, describes the last jump event in the sequence. In the anomalous phases, the statistics of meanders and excursions are essential for the calculation of the mean square displacement, showing that our correction to the MW equation is crucial, and points to the sensitivity of the transport on a single jump event. Our work provides relations between the statistics of velocity excursions and meanders and that of the diffusivity.Comment: Supersedes arXiv: 1305.008

Credit constraints, cyclical fiscal policy and industry growth

This paper evaluates whether the cyclical pattern of fiscal policy can affect growth. We first build a simple endogenous growth model where entrepreneurs can invest either in short-run projects or in long-term growth enhancing projects. Long-term projects involve a liquidity risk which credit constrained firms try to overcome by borrowing on the basis of their short-run profits. By increasing firms' market size in recessions, a countercyclical fiscal policy will boost investment in productivity-enhancing long-term projects, and the more so in sectors that rely more on external financing or which display lower asset tangibility. Second, the paper tests this prediction using Rajan and Zingales (1998)'s diff-and-diff methodology on a panel data sample of manufacturing industries across 17 OECD countries over the period 1980-2005. The evidence confirms that the positive effects of a more countercyclical fiscal policy on value added growth, productivity growth, and R&D expenditure, are indeed larger in industries with heavier reliance on external finance or lower asset tangibility

The effects of entry on incumbent innovation and productivity

How does firm entry affect innovation incentives in incumbent firms? Microdata suggest that there is heterogeneity across industries. Specifically, incumbent productivity growth and patenting is positively correlated with lagged greenfield foreign firm entry in technologically advanced industries, but not in laggard industries. In this paper we provide evidence that these correlations arise from a causal effect predicted by Schumpeterian growth theory—the threat of technologically advanced entry spurs innovation incentives in sectors close to the technology frontier, where successful innovation allows incumbents to survive the threat, but discourages innovation in laggard sectors, where the threat reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro panel data for the United Kingdom. We control for the endogeneity of entry by exploiting major European and U.K. policy reforms, and allow for endogeneity of additional factors. We complement the analysis for foreign entry with evidence for domestic entry and entry through imports

Infinite ergodic theory meets Boltzmann statistics

We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at large length scales. The partition function diverges and hence the standard canonical ensemble fails. This is replaced with tools stemming from infinite ergodic theory. Boltzmann-Gibbs statistics, even though not normalized, still describes integrable observables, like energy and occupation times. The Boltzmann infinite density is derived heuristically using an entropy maximization principle, as well as via a first-principles calculation using an eigenfunction expansion in the continuum of low-energy states. A generalized virial theorem is derived, showing how the virial coefficient describes the delay in the diffusive spreading of the particles, found at large distances. When the process is non-recurrent, e.g. diffusion in three dimensions with a Coulomb-like potential, we use weighted time averages to restore basic canonical relations between time and ensemble averages. (C) 2020 Elsevier Ltd. All rights reserved

Anomalous diffusion in the citation time series of scientific publications

We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse anomalously, their variance scales with time proportional to t (2H ), where H not equal 1/2. We provide detailed analysis of the various factors that lead to the anomalous behavior: non-stationarity, long-ranged correlations and a fat-tailed increment distribution. The papers exhibit a high degree of heterogeneity across the various fields, as the statistics of the highest cited papers is fundamentally different from that of the lower ones. The citation data is shown to be highly correlated and non-stationary; as all the papers except the small percentage of them with high number of citations, die out in time

Moses, Noah and Joseph effects in Levy walks

We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the 'Joseph effect' (Mandelbrot and Wallis 1968 Water Resour. Res.4 909), fat-tails of the increment probability density lead to a 'Noah effect' (Mandelbrot and Wallis 1968 Water Resour. Res.4 909), and non-stationarity, to the 'Moses effect' (Chen et al 2017 Phys. Rev. E 95 042141). After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled Levy walk, compare our results to theoretical predictions, and discuss the generality of the method

Local equilibrium properties of ultraslow diffusion in the Sinai model

We perform numerical studies of a thermally driven, overdamped particle in a random quenched force field, known as the Sinai model. We compare the unbounded motion on an infinite 1-dimensional domain to the motion in bounded domains with reflecting boundaries and show that the unbounded motion is at every time close to the equilibrium state of a finite system of growing size. This is due to time scale separation: inside wells of the random potential, there is relatively fast equilibration, while the motion across major potential barriers is ultraslow. Quantities studied by us are the time dependent mean squared displacement, the time dependent mean energy of an ensemble of particles, and the time dependent entropy of the probability distribution. Using a very fast numerical algorithm, we can explore times up top 10(17) steps and thereby also study finite-time crossover phenomena

Explaining Africa’s public consumption procyclicality : revisiting old evidence

This paper compiles a novel dataset of time-varying measures of government consumption cyclicality for a panel of 46 African economies between 1960 and 2014. Government consumption has, generally, been highly procyclical over time in this group of countries. However, sample averages hide serious heterogeneity across countries with the majority of them showing procyclical behavior despite some positive signs of graduation from the “procyclicality trap” in a few cases. By means of weighted least squares regressions, we find that more developed African economies tend to have a smaller degree of government consumption procyclicality. Countries with higher social fragmentation and those are more reliant on foreign aid inflows tend to have a more procyclical government consumption policy. Better governance promotes counter- cyclical fiscal policy whileincreased democracy dampens it. Finally, some fiscal rules are important in curbing the procyclical behavior of government consumption.info:eu-repo/semantics/publishedVersio

Corporate Hierarchies and the Size of Nations: Theory and Evidence

Corporate organization varies within a country and across countries with country size. The paper starts by establishing some facts about corporate organization based on unique data of 660 Austrian and German corporations. The larger country (Germany) has larger firms with flatter more decentral corporate hierarchies compared to the smaller country (Austria). Firms in the larger country change their organization less fast than firms in the smaller country. Over time firms have been introducing less hierarchical organizations by delegating power to lower levels of the corporation. We develop a theory which explains these facts and which links these features to the trade environment that countries and firms face. We introduce firms with internal hierarchies in a Krugman (1980) model of trade. We show that international trade and the toughness of competition in international markets induce a power struggle in firms which eventually leads to decentralized corporate hierarchies. We offer econometric evidence which is consistent with the models predictions