On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.Comment: 25 pages, published in Journal of Mathematical Physic

Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture

This paper revisits the question of reconstructing bulk gauge fields as boundary operators in AdS/CFT. In the presence of the wormhole dual to the thermofield double state of two CFTs, the existence of bulk gauge fields is in some tension with the microscopic tensor factorization of the Hilbert space. I explain how this tension can be resolved by splitting the gauge field into charged constituents, and I argue that this leads to a new argument for the "principle of completeness", which states that the charge lattice of a gauge theory coupled to gravity must be fully populated. I also claim that it leads to a new motivation for (and a clarification of) the "weak gravity conjecture", which I interpret as a strengthening of this principle. This setup gives a simple example of a situation where describing low-energy bulk physics in CFT language requires knowledge of high-energy bulk physics. This contradicts to some extent the notion of "effective conformal field theory", but in fact is an expected feature of the resolution of the black hole information problem. An analogous factorization issue exists also for the gravitational field, and I comment on several of its implications for reconstructing black hole interiors and the emergence of spacetime more generally.Comment: 26 pages plus appendices, 8 figures. v2: minor clarifications/corrections, references adde

Agent-Based Models and Simulations in Economics and Social Sciences: from conceptual exploration to distinct ways of experimenting

Now that complex Agent-Based Models and computer simulations spread over economics and social sciences - as in most sciences of complex systems -, epistemological puzzles (re)emerge. We introduce new epistemological tools so as to show to what precise extent each author is right when he focuses on some empirical, instrumental or conceptual significance of his model or simulation. By distinguishing between models and simulations, between types of models, between types of computer simulations and between types of empiricity, section 2 gives conceptual tools to explain the rationale of the diverse epistemological positions presented in section 1. Finally, we claim that a careful attention to the real multiplicity of denotational powers of symbols at stake and then to the implicit routes of references operated by models and computer simulations is necessary to determine, in each case, the proper epistemic status and credibility of a given model and/or simulation

Institutional mimesis: an experimental study on the grounding of legal concepts

Legal institutions, legal systems, law in general are human artefacts: Not only they are human-dependent entities—a lot of things are human-dependent and are not artefacts: pollution, for example—, but they are created by humans as the object and outcome of a specific, intentional process of creation. This is an idea that can be seen as an assumption of both legal positivism and legal realism. Indeed, one could say that these two traditional conceptions decline in different ways the same artefactual nature of law: On the one hand, legal positivism focuses on the fact that law is an artefact created by an authority; on the other hand, legal realism focuses on the fact that law is an artefact whose functioning requires recognition and enforcement, and whose purpose and plan must be continuously adapted through a process of interpretation and re-interpretation

Why some clusters succeed whereas others decline ? Modelling the ambivalent stability properties of clusters

The aim of this paper is to study the ambivalent properties of stabilities of clusters. We propose to enter the black box of the local knowledge externalities by focusing on the location decision externalities. In particular, we show that the nature of mimetic strategies in the convergence process of locational choices influence the dynamic stability of clusters. Thus, when uncertainty and search for legitimacy prevail on the need for coordination and the associated necessities of compatibility and technological convergence, the clusters are unstable, due to an excess of cognitive proximity and a risk of unintended spillovers. Nevertheless, this search for legitimacy, through the strategy which consists in following the locational choice of companies leader of a sector, can lead to the fast emergence of a cluster. But without relational proximity, its stability is not insured. These results are obtained following the formulation of some theoretical proposals on the links between location decision externalities and the resulting forms of socioeconomic proximities. This set of proposals is validated firstly by a model of simulation which makes it possible to test the properties of stability of aggregate outcomes of locational choices. Secondly, they are illustrated by a comparative empirical analysis of two main French clusters (Silicon Sentier and Sophia-Antipolis)..clusters, proximities, stability, location under decision externalities, Silicon Sentier, Sophia-Antipolis

Aspects of Multilinear Harmonic Analysis Related to Transversality

The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform, multilinear oscillatory integrals, multilinear geometric inequalities, multilinear Radon-like transforms, and the interplay between them.Comment: 28 pages. Article based on a short course given at the 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, 201