Lieb-Robinson Bounds and Existence of the Thermodynamic Limit for a Class of Irreversible Quantum Dynamics

We prove Lieb-Robinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with time-dependent generators that satisfy a suitable decay condition in space.Comment: Added 3 references and comments after Theorem 2; corrected typo

The equilibrium states for a model with two kinds of Bose condensation

We study the equilibrium Gibbs states for a Boson gas model, defined by Bru and Zagrebnov, which has two phase transitions of the Bose condensation type. The two phase transitions correspond to two distinct mechanisms by which these condensations can occur. The first (non-conventional) Bose condensation is mediated by a zero-mode interaction term in the Hamiltonian. The second is a transition due to saturation quite similar to the conventional Bose-Einstein (BE) condensation in the ideal Bose gas. Due to repulsive interaction in non-zero modes the model manifests a generalized type III, i.e., non-extensive BE condensation. Our main result is that, as in the ideal Bose gas, the conventional condensation is accompanied by a loss of strong equivalence of the canonical and grand canonical ensembles whereas the non-conventional one, due to the interaction, does not break the equivalence of ensembles. It is also interesting to note that the type of (generalized) condensate, I, II, or III (in the terminology of van den Berg, Lewis and Pule), has no effect on the equivalence of ensembles. These results are proved by computing the generating functional of the cyclic representation of the Canonical Commutation Relation (CCR) for the corresponding equilibrium Gibbs states.Comment: 1+28 pages, LaTe

Synthetic turbulence modelling for offshore wind farm engineering models using coherence aggregation

Turbulent wind fields are known to be a major driver for structural loads and power fluctuations on offshore wind turbines. At the single-turbine scale, there exist well-established design standards based on wind spectra and coherence functions calibrated from years of measurements, which are used to generate multiple 10-min wind field realisations known as synthetic turbulence boxes, themselves used as input to turbine-scale aero-hydro-servo elastic codes. These methods are however not directly applicable at farm scale. When analysing the dynamics of large offshore wind farms, measurements reveal the importance of large, low-frequency turbulent vortices for power fluctuations and hence for wind farm control and grid integration. Also, farm-scale wind fields are needed as input to farm-scale aero-servo-elastic codes for the modelling of wake dynamics, affecting structural loads. These new concerns motivate an upgrade in the original turbine-scale wind field representation: (1) spectral models need to be based on farm-scale measurements, (2) the frozen-turbulence assumption merging temporal and along-wind coherence must be lifted, (3) simplifications are needed to reduce the number of degrees of freedom as the domain becomes excessively large. This paper suggests models and algorithms for aggregated farm-wide corrrelated synthetic turbulence generation—lumping the wind field into space-averaged quantities—adapted to the aero-hydro-servo elastic modelling of large offshore wind farms. Starting from the work of Sørensen et al. in the early 2000s for grid integration purposes, methods for structural load modelling (through wake meandering and high-resolution wind field reconstruction) are introduced. Implementation and efficiency matters involving mathematical subtleties are then presented. Finally, numerical experiments are carried out to (1) verify the approach and implementation against a state-of-the-art point-based—as opposite to aggregated—synthetic turbulence generation code and (2) illustrate the benefit of turbulence aggregation for the modelling of large offshore wind farms.Synthetic turbulence modelling for offshore wind farm engineering models using coherence aggregationpublishedVersio

Inter-firm dependency and employment inequalities : Theoretical hypotheses and empirical tests

This article highlights the importance of power relations in inter-firm relations and analyses their impact on firms' employment management practices. We show, firstly, that the use of subcontracting creates a chain of inter-firm economic dependency because it leads the principal contractor to plan and control the activities of the subcontractors. We then advance the hypothesis that this chain of dependency influences both the skill structure and wage levels. Empirical tests carried out on French data confirm that firms that subcontract outsource execution tasks and that the hierarchy of firms impacts employees' wage levels.Subcontracting ; skills ; wages ; power relation

Asymptotic Behaviour of Semigroup Traces and Schatten Classes of Resolvents

Motivated by examples from physics and noncommutative geometry, given a generator $A$ of a Gibbs semigroup, we reexamine the relationship between the Schatten class of its resolvents and the behaviour of the norm-trace \norm{e^{-tA}}_1\, when $t$ approaches zero. In addition to applying Tauberian results, we specifically investigate the compatibility of asymptotic behaviours with derivations and perturbations. Along the course of our study, we present a novel characterisation of Gibbs semigroups.Comment: 45 page

Functional Expansions

Path dependence is omnipresent in social science, engineering, and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often infinite-dimensional, thus challenging from a conceptual and computational perspective. In this work, we shed light on expansions of functionals. First, we treat static expansions made around paths of fixed length and propose a generalization of the Wiener series$-$the intrinsic value expansion (IVE). In the dynamic case, we revisit the functional Taylor expansion (FTE). The latter connects the functional It\^o calculus with the signature to quantify the effect in a functional when a "perturbation" path is concatenated with the source path. In particular, the FTE elegantly separates the functional from future trajectories. The notions of real analyticity and radius of convergence are also extended to the path space. We discuss other dynamic expansions arising from Hilbert projections and the Wiener chaos, and finally show financial applications of the FTE to the pricing and hedging of exotic contingent claims.Comment: 39 pages, 7 figure

J.-P. Paulet (dir.), 2000, Les très grandes villes dans le monde

Cet ouvrage propose aux lecteurs des réflexions sur l’explosion urbaine de la deuxième moitié du XXe siècle, avec une analyse sur la complexité des espaces agglomérés, sur les limites urbaines et les incidences sociales des grandes villes. Les aspects relatifs au fonctionnement et à la gestion durable de ces grandes entités urbaines aux formes imprécises sont également analysés. Les éditions SEDES ont l’ambition de publier, chaque année, une synthèse sur les thèmes mis au programme des concou..

J.-P. Paulet (dir.), 2000, Les très grandes villes dans le monde

Cet ouvrage propose aux lecteurs des réflexions sur l’explosion urbaine de la deuxième moitié du XXe siècle, avec une analyse sur la complexité des espaces agglomérés, sur les limites urbaines et les incidences sociales des grandes villes. Les aspects relatifs au fonctionnement et à la gestion durable de ces grandes entités urbaines aux formes imprécises sont également analysés. Les éditions SEDES ont l’ambition de publier, chaque année, une synthèse sur les thèmes mis au programme des concou..

La sous-traitance comme moyen de subordination réelle de la force de travail

France has witnessed a significant rise in the recourse to sub-contracting over the last twenty years. However the latter is not to be seen as a response to the supposedly growing instability of the economic environment. It is primarily a further stage in the effective subordination of labour to capital. The replacement of direct labour by a commercial relation is used in order to bypass the framework of social legislation which labour had established through its struggles. Contrary to the formal fragmentation of collective labour, capital has maintained its unity and its control of the process of production. Capital thus becomes even more hierarchical, by way of its wilful invocation of an alleged “market constraint”, the aim of which is to engineer a new disciplining of the labour force.La sous-traitance a connu un essor considérable depuis vingt ans en France. Ces pratiques ne sont pas une réponse à l'instabilité supposée croissante de l'environnement économique. Elles représentent surtout une nouvelle étape dans la subordination réelle de la force de travail au capital. La substitution d'une relation commerciale à du travail direct est utilisée pour contourner les protections instituées de haute lutte par le salariat. Au delà de l'éclatement formel du travailleur collectif, le capital garde son unité face au travail et sa maîtrise du procès de production. Il se hiérarchise encore davantage en introduisant de toute pièce une «contrainte de marché» destinée à produire une nouvelle discipline de la force de travail