Critical phenomena and renormalization-group flow of multi-parameter \Phi^4 field theories

In the framework of the renormalization-group (RG) approach, critical phenomena can be investigated by studying the RG flow of multi-parameter $\Phi^4$ field theories with an $N$-component fundamental field, containing up to 4th-order polynomials of the field. Some physically interesting systems require $\Phi^4$ field theories with several quadratic and quartic parameters, depending essentially on their symmetry and symmetry-breaking pattern at the transition. Results for their RG flow apply to disorder and/or frustrated systems, anisotropic magnetic systems, density wave models, competing orderings giving rise to multicritical behaviors. The general properties of the RG flow in multi-parameter $\Phi^4$ field theories are discussed. An overview of field-theoretical results for some physically interesting cases is presented, and compared with other theoretical approaches and experiments. Finally, this RG approach is applied to investigate the nature of the finite-temperature transition of QCD with $N_f$ light quarks.Comment: 22 pages, Plenary talk at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings

We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of the kind of spans known as butterflies and, conversely, these data determine a bimonoidal functor. We extend this result to $n$-variables, and prove that, in a manner analogous to that of butterflies, these multi-extensions can be composed. This is phrased in terms of a multilinear functor calculus in a bicategory. As an application, we study a bimonoidal category or stack, treating the multiplicative structure as a bimonoidal functor with respect to the additive one. In the context of the multilinear functor calculus, we view the bimonoidal structure as an instance of the general notion of pseudo-monoid. We show that when the structure is ring-like, i.e. the pseudo-monoid is a stack whose fibers are categorical rings, we can recover the classification by the third Mac Lane cohomology of a ring with values in a bimodule.Comment: Accepted version to appear in Theory and Applications of Categories; 61 Pages; the new Appendix E contains the full hypercohomology computation of the characteristic class of a ring-like stac

Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

We investigate the particle-number dependence of some features of the out-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime. We consider protocols entailing the variation of the external potential which confines the particles within a limited spatial region, in particular sudden changes of the trap size. In order to characterize the dynamic behavior of the Fermi gas, we consider various global quantities such as the ground-state fidelity for different trap sizes, the quantum work statistics associated with the protocol considered, and the Loschmidt echo measuring the overlap of the out-of-equilibrium quantum states with the initial ground state. Their asymptotic particle-number dependences show power laws for noninteracting Fermi gases. We also discuss the effects of short-ranged interactions to the power laws of the average work and its square fluctuations, within the Hubbard model and its continuum limit, arguing that they do not generally change the particle-number power laws of the free Fermi gases, in any spatial dimensions.Comment: 16 pages, 5 fig

A gravitational collapse singularity theorem that improves Penrose's

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in absence of predictability and hence compatibly with quatum field theory and black hole evaporation.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Hermitian-holomorphic (2)-Gerbes and tame symbols

We observe that the line bundle associated to the tame symbol of two invertible holomorphic functions also carries a fairly canonical hermitian metric, hence it represents a class in a Hermitian holomorphic Deligne cohomology group. We put forward an alternative definition of hermitian holomorphic structure on a gerbe which is closer to the familiar one for line bundles and does not rely on an explicit ``reduction of the structure group.'' Analogously to the case of holomorphic line bundles, a uniqueness property for the connective structure compatible with the hermitian-holomorphic structure on a gerbe is also proven. Similar results are proved for 2-gerbes as well. We then show the hermitian structures so defined propagate to a class of higher tame symbols previously considered by Brylinski and McLaughlin, which are thus found to carry corresponding hermitian-holomorphic structures. Therefore we obtain an alternative characterization for certain higher Hermitian holomorphic Deligne cohomology groups.Comment: Sections on comparisons for hermitian connective structures added at referee's request. Some new results on compatibility between hermitian and analytic connective structure

Work, education and scientific and technological development knowledge and training

A new facet of the productive structures is the accrued importance of the component "knowledge and training". Indeed, knowledge and training become parts of the productive process from the beginning to its marketing, the traditional vocational training being a limited part of the activities regarding knowledge and transfer inside the working place. At the same time, educational systems come more and more to resemble productive systems; first of all, because their employees are, in many countries, the most relevant part of the working force, secondly, because their "products" are quite often evaluated by the market; thirdly, because part of these educational systems are integrated in the productive system itself. As productive systems, educational systems are facing the same problems as any other productive system: skilling and deskilling, introduction of technologies, explosions hierarchization, etc.peer-reviewe

Stacks of Ann-Categories and their morphisms

We show that $\mathit{ann}$-categories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. More precisely, we prove the groupoid of morphisms between two $\mathit{ann}$-categories is equivalent to that of bimodule butterflies between the presentations. A bimodule butterfly is a specialization of a butterfly, i.e. a special kind of span or fraction, between the underlying complexesComment: 23 pages. One added section on the class of a stack of ann-categories and Shukla cohomology. One appendix includes an argument courtesy of T. Pirashvili showing the equivalence between Shukla and Andr\'e-Quillen cohomology for associative algebras, when Shukla cohomology is defined via a model structure on DGA

Getting out of the car: an institutional/evolutionary approach to sustainable transport policies

Orthodox economics sees transport as a market which can be made more sustainable by improving its self-regulating capacity. To date this static approach has not been able to limit the growing demand for transport and its increasing environmental impact. Better results might be obtained by using evolutionary and institutional economics. Starting from these theories, a sustainable transport policy should be based on three fundamental considerations. First, transport is not a market, but a sum of systems affected by path-dependence and lock-in phenomena. Second, transport is not sustainable because it is locked in environmentally sub-optimal systems. Third, structural changes in technologies and organisations, institutions, and values are needed to establish more sustainable transport systems. We give an example of the use of an institutional/evolutionary approach to sustainable transport policies in the transition from the system of mass motorisation to the new urban mobility system

Financial liberalization and contagion with unobservable savings

How do market-based channels for the provision of liquidity affect financial liberalization and contagion? In order to answer this question, I extend the Diamond and Dybvig (1983) model of financial intermediation to a two-country environment with unobservable markets for borrowing and lending and comparative advantages in the investment technologies. I demonstrate that the role of hidden markets crucially depends on the level of financial integration of the economy. Despite always imposing a burden on intermediaries, unobservable markets allow agents to partially enjoy gains from financial integration when interbank markets are autarkic. In fully liberalized systems such effect instead disappears. Similarly, in autarky the distortion created by hidden markets improve the resilience of the system to unexpected liquidity shocks. With fully integrated interbank markets, such effect again disappears, as unexpected liquidity shocks always lead to bankruptcy and contagion.financial intermediation, financial liberalization, financial contagion, unobservable savings