Level density of a Bose gas: beyond the saddle point approximation

The present article is concerned with the use of approximations in the calculation of the many-body density of states (MBDS) of a system with total energy E, composed by N bosons. In the mean-field framework, an integral expression for MBDS, which is proper to be performed by asymptotic expansions, can be derived. However, the standard second order steepest descent method cannot be applied to this integral when the ground-state is sufficiently populated. Alternatively, we derive a uniform formula for MBDS, which is potentially able to deal with this regime. In the case of the one-dimensional harmonic oscillator, using results found in the number theory literature, we show that the uniform formula improves the standard expression achieved by means of the second order method

Scaling Function, Universality and Analytical Solutions of Generalized One-Species Population Dynamics Models

We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one is able to demonstrate that their ratio with respect to its initial value is universal. This ratio is independent from the initial condition and from the model parameters. Although the effort rate does not break the model universality it produces a transition between the species extinction and survival. A general formula is furnished to obtain the scaling functions.Comment: 8 pages and 4 figure

The Double Effect Doctrine in Thomas Aquinas' Just War

The use of war to expand the limits of Christianity or the limits of the power of the Christian Church was, from an early age, regular. This theme, which over the centuries has been the subject of intense debates among intellectuals who tried to justify the morality of this war or, by contrast, served to develop various attacks on the Church, is the focus of the present work. In this way, we seek to understand here the development of the concept of just war in St. Thomas Aquinas Summa Theologiae, it's way of justifying the use of war, the moments when its use is legitimate, the applicability of the Double Effect Doctrine in this concept and also the influence that his thought exercised on chronologically closer thinkers, but also contemporary philosophy, using to this purpose, the work of Elizabeth Anscombe, a striking figure in twentieth-century philosophy, to understand the pertinence of the medieval theologian thought in this matter.El uso de la guerra para expandir los límites del cristianismo o los límites del poder de la Iglesia cristiana fue, desde temprana edad, regular. Este tema, que a lo largo de los siglos ha sido objeto de intensos debates entre intelectuales que intentaron justificar la moralidad de esta guerra o, por el contrario, sirvió para desarrollar varios ataques contra la Iglesia, es el foco del presente trabajo. De esta manera, buscamos comprender aquí el desarrollo del concepto de guerra justa en la Summa Theologiae de Santo Tomás de Aquino, su forma de justificar el uso de la guerra, los momentos en que su uso es legítimo, la aplicabilidad de la Doctrina del Doble Efecto en este concepto y también la influencia que ejerció su pensamiento en los pensadores cronológicamente más cercanos, pero también en la filosofía contemporánea, utilizando para este propósito, el trabajo de Elizabeth Anscombe, una figura sorprendente en la filosofía del siglo XX, para comprender la pertinencia de lo pensamiento del teólogo medieval en este asunto

Three Essays on Energy Economics

This dissertation consists of three essays that explore empirical issues concerning energy prices in the United States. In particular, it analyzes the price transmission within and across different energy markets and their interactions with the overall economy. The first essay evaluates the dynamic spatial integration in the U.S. natural gas market and the relative importance of each location in the overall price discovery process. I show that the regional natural gas market is on average well-integrated in both the short- and long-runs, although market integration has declined over the past few years due to pipeline capacity constraints in an increasingly oversupplied market. In the second essay, I evaluate the effect of economic policy uncertainty on the volatility pattern in U.S. crude oil and natural gas markets, as well as how this relationship has changed in an era of abundant market supply. Natural gas and crude oil present heterogeneous volatility regimes (i.e., high vs. low volatility), in which the volatility persistence for crude oil is similar during the pre- and post-shale era, while natural gas presented significant regime changes. Economic policy uncertainty exerts a positive and significant effect on the likelihood of the high-volatility regime for both markets. However, the effect has declined after 2010, possibly reflecting the large and more efficient production of fossil fuels in the country which allows producers and investors to respond more rapidly to market shocks. Finally, the third essay revisits three important open questions in the energy economics literature, namely, the “decoupling” of crude oil and natural gas prices, the mixed relationship between natural gas and electricity prices, and the “rockets and feathers” effect between crude oil and petroleum product prices. Empirically, I analyze the directional price return predictability between various energy markets at different quantiles of their respective price return distributions. I find positive and significant spillover effects from crude oil to natural gas during bearish market conditions, which have weakened after 2013, suggesting a possible “delink” between the two markets in recent years. For the relationship between natural gas and electricity price returns, results suggest a bi-directional spillover at moderate and high return quantiles. In recent years, the two markets appear to have become more correlated during bearish market conditions, reflecting the increasing importance of natural gas as an input to produce electricity and the transition of natural gas from peak load to baseload power sources. Finally, no evidence is found for the “rockets and feathers” effect from crude oil to either gasoline or heating oil market