Deriving the hard thermal loops of QCD from classical transport theory

Classical transport theory is employed to analyze the hot quark-gluon plasma at the leading order in the coupling constant. A condition on the (covariantly conserved) color current is obtained. From this condition, the generating functional of hard thermal loops with an arbitrary number of soft external bosonic legs can be derived. Our approach, besides being more direct than alternative ones, shows that hard thermal loops are essentially classical.

Planning under partial observability by classical replanning: theory and experiments

Planning with partial observability can be formulated as a non-deterministic search problem in belief space. The problem is harder than classical planning as keeping track of beliefs is harder than keeping track of states, and searching for action policies is harder than searching for action sequences. In this work, we develop a framework for partial observability that avoids these limitations and leads to a planner that scales up to larger problems. For this, the class of problems is restricted to those in which 1) the non-unary clauses representing the uncertainty about the initial situation are nvariant, and 2) variables that are hidden in the initial situation do not appear in the body of conditional effects, which are all assumed to be deterministic. We show that such problems can be translated in linear time into equivalent fully observable non-deterministic planning problems, and that an slight extension of this translation renders the problem solvable by means of classical planners. The whole approach is sound and complete provided that in addition, the state-space is connected. Experiments are also reported.

Reliable computation of robust response tori on the verge of breakdown

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Current Account imbalances, thriftiness and the real exchange rate in a growing economy

This paper analyses the theoretical relevance of the dynamical aspects of growth on the discussion about the observed positive correlation between per capita real income and real exchange rates. With this purpose, we develop a simple exogenous growth model where the internal, external and intertemporal equilibrium conditions of a typical macroeconomic model are imposed; this last one through the inclusion of a balanced growth path for the foreign assets accumulation. The main result under this consideration is that the relationship defended by the Balassa-Samuelson hypothesis is no more so straightforward. In our particular approach, the mentioned bilateral relationship depends on a parameter measuring thriftiness in the economy. Therefore, the probability of ending up with a positive relationship between growth and real exchange rates -as the classical economic theory predicts- will be higher when the economy is able to maintain a minimum saving ratio. Moreover, given that our model considers a simple Keynesian consumption function, some explosive paths can also be possible.

Resonant spin tunneling in small antiferromagnetic particles

The paper reports a detailed experimental study on magnetic relaxation of natural horse-spleen ferritin. ac susceptibility measurements performed on three samples of different concentration show that dipole-dipole interactions between uncompensated moments play no significant role. Furthermore, the distribution of relaxation times in these samples has been obtained from a scaling of experimental X" data, obtained at different frequencies. The average uncompensated magnetic moment per protein is compatible with a disordered arrangement of atomic spins throughout the core, rather than with surface disorder. The observed field dependence of the blocking temperature suggests that magnetic relaxation is faster at zero field than at intermediate field values. This is confirmed by the fact that the magnetic viscosity peaks at zero field, too. Using the distribution of relaxation times obtained independently, we show that these results cannot be explained in terms of classical relaxation theory. The most plausible explanation of these results is the existence, near zero field, of resonant magnetic tunneling between magnetic states of opposite orientation, which are thermally populated.

Microstructural evolution of primary crystallization in diffusion-controlled grain growth

A model has been developed for evaluating grain size distributions in primary crystallizations where the grain growth is diffusion controlled. The body of the model is grounded in a recently presented mean-field integration of the nucleation and growth kinetic equations, modified conveniently in order to take into account a radius-dependent growth rate, as occurs in diffusion-controlled growth. The classical diffusion theory is considered, and a modification of this is proposed to take into account interference of the diffusion profiles between neighbor grains. The potentiality of the mean-field model to give detailed information on the grain size distribution and transformed volume fraction for transformations driven by nucleation and either interface- or diffusion-controlled growth processes is demonstrated. The model is evaluated for the primary crystallization of an amorphous alloy, giving an excellent agreement with experimental data. Grain size distributions are computed, and their properties are discussed.

Renormalization of gauge-invariant operators and the axial anomaly

The renormalization properties of gauge-invariant composite operators that vanish when the classical equations of motion are used (class II^a operators) and which lead to diagrams where the Adler-Bell-Jackiw anomaly occurs are discussed. It is shown that gauge-invariant operators of this kind do need, in general, nonvanishing gauge-invariant (class I) counterterms.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.

Where Has the Old Debate Gone? Realism, Institutionalism, and IR Theory

This paper resorts to the contribution of the science philosopher Gerald Holton to map some of the IR arguments and debates in an unconventional and more insightful way. From this starting point, it is sustained that the formerly all-pervading neorealism-neoinstitutionalism debate has lost its appeal and is attracting less and less interest among scholars. It does not structure the approach of the theoretically-oriented authors any more; at least, not with the habitual intensity. More specifically, we defend that the neo-neo rapprochement, even if it could have demonstrated that international cooperation is possible and relevant in a Realist world, it has also impoverished theoretical debate by hiding some of the most significant issues that preoccupied classical transnationalists. Hence, some authors appear to be trying to rescue some of these arguments in an analytical and systematic fashion, opening up a theoretical querelle that may be the next one to pay attention to.

The Core ideas and axioms of classical fascism (1919-1945)

This article presents and explores the axioms and core ideas, or idées-force, of the Fascist ideologies of the first third of the twentieth century. The aim is to identify the features that define the term “Classical Fascism” as a conceptual category in the study of politics and to uncover the core ideas of its political theory. This analysis requires an appraisal of both the idées-force themselves and the political use that is made of them. If these appreciations are correct, Classical Fascism is characterized by a set of ideological and political aims and methods in which ideas, attitudes and behaviours are determined by an anti-democratic palingenetic ultranationalism underpinned by a sacralized ideology; the quest for a united, indissoluble society as apolitical system and, at the same time, the collective myth that mobilizes and redeems the nation; and third, violence as a political vehicle applied unchecked against internal opposition and against external enemies who challenge the nation´s progression towards the dream of rebirth and the culmination of this progression in the form of an empire.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Generalized descriptive set theory and classification theory

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria delsConjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics espotencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funciódensitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps queles distribucions de probabilitat quàntiques