Spectral dimension of a quantum universe

In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal length by averaging the graininess of the quantum manifold in the flat space case. As a result we obtain that, for large diffusion times, the quantum spacetime behaves like a smooth differential manifold of discrete dimension. On the other hand, for smaller diffusion times, the spacetime looks like a fractal surface with a reduced effective dimension. For the specific case in which the diffusion time has the size of the minimal length, the spacetime turns out to have a spectral dimension equal to 2, suggesting a possible renormalizable character of gravity in this regime. For smaller diffusion times, the spectral dimension approaches zero, making any physical interpretation less reliable in this extreme regime. We extend our result to the presence of a background field and curvature. We show that in this case the spectral dimension has a more complicated relation with the diffusion time, and conclusions about the renormalizable character of gravity become less straightforward with respect to what we found with the flat space analysis.Comment: 5 pages, 1 figure, references added, typos corrected, title changed, final version published in Physical Review

WAS MALTHUS RIGHT? A VAR ANALYSIS OF ECONOMIC AND DEMOGRAPHIC INTERACTIONS IN PRE-INDUSTRIAL ENGLAND

This paper shows that the interaction between economic and demographic variables in England before the onset of modern economic growth did not fit some crucial assumptions of the Malthusian model. I estimated a vector autoregression for data on fertility, nuptiality, mortality and real wages over the period 1541-1840 applying a well-known identification strategy broadly used in macroeconomics. The results show that endogenous adjustment of population to real wages functioned as Malthus assumed only until the 17th century: positive checks disappeared during the 17th century and preventive checks disappeared before 1740. This implies that the endogenous adjustment of population levels to changes in real wages -one of the cornerstones of the Malthusian model- did not work during an important part of the period usually considered within the “Malthusian regime”.

Charged rotating noncommutative black holes

In this paper we complete the program of the noncomutative geometry inspired black holes, providing the richest possible solution, endowed with mass, charge and angular momentum. After providing a prescription for employing the Newman-Janis algorithm in the case of nonvanishing stress tensors, we find regular axisymmetric charged black holes in the presence of a minimal length. We study also the new thermodynamics and we determine the corresponding higher-dimensional solutions. As a conclusion we make some consideration about possible applications.Comment: 13 pages, 3 figures, correction of a typesetting inattention, updated reference list, version accepted for publication on Physical Review

A model of radiating black hole in noncommutative geometry

The phenomenology of a radiating Schwarzschild black hole is analyzed in a noncommutative spacetime. It is shown that noncommutativity does not depend on the intensity of the curvature. Thus we legitimately introduce noncommutativity in the weak field limit by a coordinate coherent state approach. The new interesting results are the following: i) the existence of a minimal non-zero mass to which black hole can shrink; ii) a finite maximum temperature that the black hole can reach before cooling down to absolute zero; iii) the absence of any curvature singularity. The proposed scenario offers a possible solution to conventional difficulties when describing terminal phase of black hole evaporation.Comment: 10 pages, 4 figure

Adult mortality and investment: a new explanation of the English agricultural productivity in the 18th century.

We claim that the exogenous decline of adult mortality at the end of the seventeenth century can be one of the causes driving both the decline of interest rate and the increase in agricultural production per acre in preindustrial England. Following the intuition of the life-cycle hypothesis, we show that the increase in adult life expectancy must have implied less farmer impatience and it could have caused more investment in nitrogen stock and land fertility, and higher production per acre. We analyse this dynamic interaction using an overlapping generation model and show that the evolution of agricultural production and capital rates of return predicted by the model coincide fairly well with their empirical pattern.

Relativistic kinetic theory of magnetoplasmas

Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems. Such phenomena require their description in the framework of a consistent relativistic kinetic theory, rather than on relativistic MHD equations, subject to specific closure conditions. The purpose of this work is to apply the relativistic single-particle guiding-center theory developed by Beklemishev and Tessarotto, including the nonlinear treatment of small-wavelength EM perturbations which may naturally arise in such systems. As a result, a closed set of relativistic gyrokinetic equations, consisting of the collisionless relativistic kinetic equation, expressed in hybrid gyrokinetic variables, and the averaged Maxwell's equations, is derived for an arbitrary four-dimensional coordinate system.Comment: 6 pages, 1 figure. Contributed to the Proceedings of the 24th International Symposium on Rarefied Gas Dynamics, July 10-16, 2004 Porto Giardino Monopoli (Bari), Ital

Spinning Loop Black Holes

In this paper we construct four Kerr-like spacetimes starting from the loop black hole Schwarzschild solutions (LBH) and applying the Newman-Janis transformation. In previous papers the Schwarzschild LBH was obtained replacing the Ashtekar connection with holonomies on a particular graph in a minisuperspace approximation which describes the black hole interior. Starting from this solution, we use a Newman-Janis transformation and we specialize to two different and natural complexifications inspired from the complexifications of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that the space-times obtained in this way are singularity free and thus there are no naked singularities. We show that the transformation move, if any, the causality violating regions of the Kerr metric far from r=0. We study the space-time structure with particular attention to the horizons shape. We conclude the paper with a discussion on a regular Reissner-Nordstrom black hole derived from the Schwarzschild LBH and then applying again the Newmann-Janis transformation.Comment: 18 pages, 18 figure

A Methodological approach to estimating the Money Demand in Pre-Industrial Economies: Probate Inventories and Spain in the 18th century

The study of monetary phenomena and the understanding of price determination in Modern Europe are too often limited by the scarcity of good-quality data sets on the evolution across time of variables like money holdings, income, or wealth. In this paper we show that the information contained in probate inventories can be extremely useful to circumvent that problem. In particular, combining a data set of 114 inventories from Palencia (North of Spain) between 1750 and 1770 with census information (Catastro de Ensenada) we make a cross-section estimation of a money demand which is the first one ever produced for any period before the 19th century. The results provide meaningful insights about the relation between money demand and wealth, urbanization and structural change in a pre-industrial economy and highlight the potential of probate inventories to improve our knowledge of the monetary history of Modern Europe.

The exact radiation-reaction equation for a classical charged particle

An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field. The problem is related to the conjecture that for a classical charged point-particle there should exist a relativistic equation of motion (RR equation) which results both non-perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non-asymptotic, i.e., it does not depend on any infinitesimal parameter. In this paper we intend to propose a novel solution to this well known problem, and in particular to point out that the RR equation is necessarily variational. The approach is based on two key elements: 1) the adoption of the relativistic hybrid synchronous Hamilton variational principle recently pointed out (Tessarotto et al, 2006). Its basic feature is that it can be expressed in principle in terms of arbitrary "hybrid" variables (i.e., generally non-Lagrangian and non-Hamiltonian variables); 2) the variational treatment of the EM self-field, taking into account the exact particle dynamics.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

Tunneling of massive and charged particles from noncommutative Reissner-Nordstr\"{o}m black hole

Massive charged and uncharged particles tunneling from commutative Reissner-Nordstrom black hole horizon has been studied with details in literature. Here, by adopting the coherent state picture of spacetime noncommutativity, we study tunneling of massive and charged particles from a noncommutative inspired Reissner-Nordstrom black hole horizon. We show that Hawking radiation in this case is not purely thermal and there are correlations between emitted modes. These correlations may provide a solution to the information loss problem. We also study thermodynamics of noncommutative horizon in this setup.Comment: 10 pages, 2 figure